Prerequisites for Quantum Electrodynamics

[maverick280857]

Although this is usually a graduate course, I want to know what all the preqrequisites for studying it seriously are. (I've been reading Feynman, Schweber and a bit of Griffiths which pumped my interest).

I think mathematics should be calculus, group theory and all the stuff needed for QM. As for physics it looks like: CM (Lagrangian and Hamiltonian particularly), QM, some SM, classical electrodynamics. Quantum Field Theory?

Cheers
Vivek

 

[George Jones]

Quantum Electrodynamics is an example of a quantum field theory.

All the stuff you list could be required as prerequisites, Paul Halmos once wrote something like "The beginner should not be discouraged if he finds that he does not have the prerequisites for the prerequisites." at the beginning of one of his advanced math texts.

There is a http://www.oup.com/uk/catalogue/?ci=9780198520740#contents" that is at about the senior undergraduate level. It has a number of solved problems as examples, and, at the back, it gives short solutions (not just answers) to many of the exercises. This should make it good for self-study.

I have seen a more detailed Table of Contents for it somewhere on the web, but, unfortunately, I wasn't able to locate it for this post.

 

[maverick280857]

Hey George,

Thanks for your encouraging reply. Frankly speaking I did not expect such an encouraging response considering the fact that QFT is taught to senior undergraduates or graduate students in most colleges across the world and most people wait to learn it the step-by-step way (not that I disagree with that outlook).

Interestingly I have read a bit of the book "Relativity, Gravitation and Cosmology" by Tai-Pei Cheng which is in the same series as the book you have recommended. But I have not been able to locate this QFT book so far.

Cheers
Vivek

 

[Norman]

I have actually heard very good things about this book. My advisor likes to use it as a reference when he teaches his QFT course- personally I prefer the book by peskin and schroeder for learning QFT. It has an excellent section on QED. But, it is probably a little more rigorous mathematically than someone outside of graduate school is going to want. Who knows though.

Cheers,
Ryan

 

[maverick280857]

But can you list all the mathematics and physics prerequisites which are absolutely must? I have seen neither book yet and I don't think I can get hold of either anytime soon...

I am guessing that Group Theory, Topology, Real Analysis, Linear Algebra, Differential Geometry are some more mathematical prerequisites? (I don't know much...just gathering data randomly).

 

[George Jones]

I have actually heard very good things about this book. My advisor likes to use it as a reference when he teaches his QFT course- personally I prefer the book by peskin and schroeder for learning QFT. It has an excellent section on QED. But, it is probably a little more rigorous mathematically than someone outside of graduate school is going to want. Who knows though.

Well, I wouldn't say that the mathematics in Peskin and Schroeder is rigorous, but then there (so far) is no mathematically rigorous formulation of quantum field theory, so this is understandable.

At this level, I prefer Quantum Field Theory for Mathematicians by Robin Ticciti. This is an excellent quantum field theory book, and, in spite of its title, is not a tome on axiomatic quantum field theory, or a book that emphasizes mathematical rigour. Its presentation is, however, a little less fuzzy than presentations in many other books. It shows how to calculate physical things like cross sections, and is a serious competitor for standard works like Peskin and Schroeder. I wish this book had been available when I was a grad student!

If you have the time, I am very curious what you (or anybody else) think about this book.

I am guessing that Group Theory, Topology, Real Analysis, Linear Algebra, Differential Geometry are some more mathematical prerequisites? (I don't know much...just gathering data randomly).

I suspect that many North American grad students that study Peskin and Schroeder have not taken mathematics courses in topology, real analysis, and differential geometry. All of these courses are important for a rigorous mathematical treatment of Lie groups, but, often, the "physicists' version" of Lie groups and Lie algebras is sufficient for undertsanding the roles Lie groups play in quantum field theory.

More important is an understanding of Lagrangian and Hamiltonian dynamic, includings, possibly, a Lagrangian treatment of the elctromagnetic field.

 

[nrqed]

But can you list all the mathematics and physics prerequisites which are absolutely must? I have seen neither book yet and I don't think I can get hold of either anytime soon...

I am guessing that Group Theory, Topology, Real Analysis, Linear Algebra, Differential Geometry are some more mathematical prerequisites? (I don't know much...just gathering data randomly).

If we are talking about the minimum to understand QED, here's my two cents.

If you are at ease with quantum mechanics, then the only additional physics concepts that are required are
- Lagrangian mechanics, especially applied to fields (as George mentioned, especially the example of E&M fields).
- and a good grasp of special relativity (be at ease with four-vector notation, the concepts of spacetime intervals, relativistic dynamics (four-momentum and so on)).

As for maths, you only need to be at ease doing calculus in the complex plane (more precisely, doing integrals...so using the residue theorem, working with branch cuts, etc).

This is all you really need. You don't need group theory if you just do QED (it *is* associated to a U(1) symmetry but that's such a simple group that you don't need full-blown group theory). You don't need GR or differential geometry (unless you want to do QED in curved spacetime!).Unless you would do finite temperature field theory, you don't need thermodynamics.

I think that Griffiths' book is an excellent first step.

Just my two cents.

Patrick

EDIT: to address one of your posts, to do basic QED (i.e. not stuff in curved space-time or getting QED from string theory and that type of stuff) you don't need topology or differential geometry. And you don't need complex analysis, real analysis and linear algebra at deeper levels than what is needed in quantum mechanics. Just focus on intgegration in the complex plane, special relativity and lagrangian dynamics (especially applied to fields)

 

[George Jones]

Patrick, have you ever looked at either (Maggiore and Ticiatti) of the two very different QFT books that I mentioned. If so, what do you think? I very much like both of them, but that's just my opinion.

What are your favourite QFT books (at all levels).

 

[Norman]

I would second Patrick's statements about what math is needed to begin in basic QED. The 4-vector notation can usually be picked up pretty quickly and is typically atleast introduced quickly in a QFT book.
Good luck,
Ryan

 

[Perturbation]

But can you list all the mathematics and physics prerequisites which are absolutely must? I have seen neither book yet and I don't think I can get hold of either anytime soon...

I am guessing that Group Theory, Topology, Real Analysis, Linear Algebra, Differential Geometry are some more mathematical prerequisites? (I don't know much...just gathering data randomly).

Though there isn't much more I can add to the list of prerequisites than has already been given, I will say that teaching yourself QFT isn't as daunting as it may sound. I'm nearly 17 and got Peskin and Schroeder for Christmas. I'd been reading around various aspects of under-grad and graduate QM, electrodynamics and SR for a while and I thought it would be a good move to focus on something that unifies these approaches (in addition to Lagrangian/Hamiltonian mechanics/field theory). If you have enough knowledge about these and the maths that's used in them you can put them together and learn QFT, and QED is a pretty straight forward field theory, you can do a fair amount of QED with just relativistic quantum mechanics ("Quark and Leptons" by Halzen and Martin does this).

I will say that if you're just interested in QED as a field theory and are also looking for a more comprehensive QM text, Leslie Ballentine's is a good 'un.

Group theory would be pretty superfluous for QED, it's a pretty simple gauge theory (U(1), as nrged said). If you really wanted to know anything about groups, a few definitions would suffice, you don't need to go into further aspects of group theory to use with QED. You needn't go into performing rigorous analyses of the geometry you're using that one finds in topology and differential geometry as introductory QED texts only deal with pretty trivial geometries (namely Minkowski space-time). Some familiarity with differential geometry though would be useful just to give you a bit more insight into the subtleties of the theory, such as Lie algebras and their relations to gauge theories, the geometry of gauge bundles etc. A very good text for introducing differential geometry to the physicist is Bernard Schutz's "Geometrical Methods of Mathematical Physics", though to be honest it is lacking a little bit in the way of general bundle structures and actual Riemannian geometry, it spends a lot more time studying Lie algebras/groups, differential forms etc. Maybe someone else could recommend a more comprehensive treatment.

I think probably the only bit of maths that is of importance to QFT and that isn't hugely employed in under-grad QM is complex analysis, and the most relevant part of this is just complex contour interation.

 

[nrqed]

Patrick, have you ever looked at either (Maggiore and Ticiatti) of the two very different QFT books that I mentioned. If so, what do you think? I very much like both of them, but that's just my opinion.

No, I had never heard of neither. But I am always looking for new books on QFT (hoping that the presentation will be original and significantly different from previous books so that I will feel like I am learning something new).

I am so interested in low level presentations on QFT (because there are some basic things that I still don't understand) that I have actually ordered Maggiore a few minutes ago! Thanks for mentioning it!
So I will let you know when I get the book and have a few days to skim through it. I will look for Ticiatti as well. It sounds like it would be a worthy addition to my library!




My problem with QFT books is that I personally feel that there is too little emphasis on the conceptual basis (on the *meaning* of things). That instead, most book jump as quickly as possible to technical stuff.
I find that when one stops and starts wondering about the meaning of a lot of expressions encountered in QFT, it is not clear at all what they represent (in contrast with QM where the meaning of any given expression and its relation to possible measurements is always pretty clear).
So far, I haven't encountered any book that I find satisfying.

(as just a couple of examples...P&S say that <0|Phi(y) Phi(x)|0> (where Phi is a scalar field) is the amplitude for the propagation of a particle from x to y. And then they show that it does not vanish for spacelike events but then they add that it does not matter! Then, they say that one should show that measurements done at spacelike intervals should not affect each other and they proceed to calculate <0| [Phi(y),Phi(x)]|0> and show that this vanishes for spacelike intervals. But this seems to suggest that Phi should be considered an observable when it is not!
There are tons of things like this which are glossed over but deserve to be explained very clearly, imho.

What are your favourite QFT books (at all levels).

I must say that I am flattered that you might wonder about my opinion!
I could write several thousand words on this! But I will keep it short. The problem is that it depends a lot on one's background an dthat varies a lot even for a given person (obviously). So some books I like now would have been useless when I was starting. And some books I dislike now may start to make sense in a few months.

But A brief list:

For introductory books, I love Griffiths. I also love Aitchison and Hey (Gauge Theories in Particle Physics). I love Greiner's books on QCD and the electroweak theory so I should try to get his books on QM and on QFT and QED.

I like P&S but the conceptual explanations have left me disappointed. I find myself wishing for a book like this but written by Griffiths (someone who stops often to ask "but what does this really mean?" and "what are we trying to do here?" and so on. Someone who would explain the *idead* behind the calculations and relate them clearly to physics (is this thing an obervable? what does this state represent? What is the meaning of this amplitude? If we square it, we get a probablility which represents what? and so on). I should really get the Greiner book.

At a more advanced level, I love Hatfield (QFT ofpoint particles and strings, if I recall) because he does discuss the ideas more extensively than the vast majority of books (but not as clearly as I would like..still, it stands out in terms of discussion of the ideas and clarity of the presentation).

I like the Landau and Lif****z on QED.


I like Zee for some tidbits that are really neat but the book is unsatisfying. I think it's because when he covers stuff that one is interested in, the presentation is always too short to really learn anything. So one always feels "left on one's appetite" (as we say in French)


I also like Gross (it's not David Gross..I don't remember the exact title).


And Weinberg (vol 1).

I used to dislike Itzykson and Zuber but with a more solid background, I go back and appreciate it more and more. I never liked Kaku, however.

I know that I have more QFT books but I don't have them with me here so I am surely forgetting a bunch of them.

What about you? Any comments on the above titles? Any other titles not mentioned?
I am looking forward to receiving Maggiore.

Best regards

EDIT: I forgot Ryder! I like it as a complement (a bit like Zee but at a lower level).

 

[Astronuc]

Perhaps these are useful.

Relativity, Gravitation, and Cosmology: A Basic Introduction (Oxford Master Series in Physics) Ta-Pei Cheng (Paperback)

Table of Contents
Relativity - metric description of spacetime
1. Introduction and overview
2. Special relativity and the flat spacetime
3. The principle of equivalence
4. Metric description of a curved space
5. General relativity (GR) as a geometric theory of gravity - I
6. Spacetime outside a spherical star
Cosmology
7. The homogenous and isotropic universe
8. The expanding universe and thermal relics
9. Inflation and the accelerating universe
Relativity - full tensor formulation
10. Tensors in special relativity
11. Tensors in general relativity
12. GR as a geometric theory of gravity - II
13. Linearized theory and gravitational waves


A Modern Introduction to Quantum Field Theory (Oxford Master Series in Physics)
From the site provided by George Jones -
Table of Contents - http://www.oup.co.uk/pdf/0-19-852073-5.pdf


http://www.us.oup.com/us/catalog/general/series/OxfordMasterSeriesinPhysics/?view=usa&sf=all

Quantum Field Theory for Mathematicians Robin Ticciati

Bibliography in -
Quantum Field Theory for Mathematicians:
Background and History
http://www.math.columbia.edu/~woit/qftnotes1.pdf

 

[maverick280857]

Perhaps these are useful.

Relativity, Gravitation, and Cosmology: A Basic Introduction (Oxford Master Series in Physics) Ta-Pei Cheng (Paperback)

Thanks Astronuc. The first 3 chapters of this book are related to our first year course that has Special Relativity, so I am reading this book. As for the others, I have not seen them yet.

 

[George Jones]

Thanks Astronuc. The first 3 chapters of this book are related to our first year course that has Special Relativity, so I am reading this book. As for the others, I have not seen them yet.

My favourite pedagogical treatments of relativity are https://www.amazon.com/gp/product/0070430276/?tag=pfamazon01-20 by James Hartle. I can't say enough good things about these books.

Back to QED. In post #6, I said "there (so far) is no mathematically rigorous formulation of quantum field theory." If you are reading Schweber's QED and the Men Who Made it, look at section 9.17 to see what I mean. A few more details are given in post #17 (second paragraph), #19, and #24 in https://www.physicsforums.com/showthread.php?p=826190&highlight=dyson#post826190".

 

[George Jones]

I am always looking for new books on QFT (hoping that the presentation will be original and significantly different from previous books so that I will feel like I am learning something new).

Me too!

I am so interested in low level presentations on QFT (because there are some basic things that I still don't understand) that I have actually ordered Maggiore a few minutes ago! Thanks for mentioning it!
So I will let you know when I get the book and have a few days to skim through it. I will look for Ticiatti as well. It sounds like it would be a worthy addition to my library!

I am not sure that Maggiore will show you anything new, but I hope you like it.

I particularly like Ticciati's treatment of symmetries in chapters 3, 6, 14, 15, and 16. He take a little more mathematical care than does a typical QFT book, but I don't think that he takes so much care that physicists will be completely turned off.

My problem with QFT books is that I personally feel that there is too little emphasis on the conceptual basis (on the *meaning* of things). That instead, most book jump as quickly as possible to technical stuff.
I find that when one stops and starts wondering about the meaning of a lot of expressions encountered in QFT, it is not clear at all what they represent (in contrast with QM where the meaning of any given expression and its relation to possible measurements is always pretty clear).
So far, I haven't encountered any book that I find satisfying.

Again, I have similar feelings. I was quite sure that you felt this way, so this is one reason that I am interested in your opinions on QFT books.

(as just a couple of examples...P&S say that <0|Phi(y) Phi(x)|0> (where Phi is a scalar field) is the amplitude for the propagation of a particle from x to y. And then they show that it does not vanish for spacelike events but then they add that it does not matter! Then, they say that one should show that measurements done at spacelike intervals should not affect each other and they proceed to calculate <0|[Phi(y),Phi(x)]|0> and show that this vanishes for spacelike intervals. But this seems to suggest that Phi should be considered an observable when it is not!
There are tons of things like this which are glossed over but deserve to be explained very clearly, imho.

I don't really know enough to comment, but maybe this is relevant. If A and B are self-adjoint operators, then [A , B] =0 ==> [f(A) , f(B)] = 0 for nice functions f and g. Maybe P&S want to apply this to (not necessarily self-adjoint) field operators, so that measurements of obervables built from field observables (via the functions f and g) are guaranteed not affect each other.

For introductory books, I love Griffiths.

So do I, and I like Halzen and Martin.

I also love Aitchison and Hey (Gauge Theories in Particle Physics).

I don't have this, but I am thinking of ordering the new 2-volume edition of Aitchison and Hey. Friday afternoon I downloaded a copy of Aitchison's long pedagogical article "Nothing's plenty: The vacuum in modern quantum field theory," Contemporary Physics, 26(4), 1985. I haven't had a chance to take a look at it yet.

I love Greiner's books on QCD and the electroweak theory so I should try to get his books on QM and on QFT and QED.

I have his book Field Quantization. Lots of details.

I like P&S but the conceptual explanations have left me disappointed. I find myself wishing for a book like this but written by Griffiths (someone who stops often to ask "but what does this really mean?" and "what are we trying to do here?" and so on. Someone who would explain the *idead* behind the calculations and relate them clearly to physics (is this thing an obervable? what does this state represent? What is the meaning of this amplitude? If we square it, we get a probablility which represents what? and so on). I should really get the Greiner book.

If you find such a book, let me know!

At a more advanced level, I love Hatfield (QFT ofpoint particles and strings, if I recall) because he does discuss the ideas more extensively than the vast majority of books (but not as clearly as I would like..still, it stands out in terms of discussion of the ideas and clarity of the presentation).

Heard of it - have never looked at it.

I like the Landau and Lif****z on QED.

This was used for my graduate quantum mechanics course, and, then, I didn't like it much. Maybe if I take a look at it now, I'll like it more.

I like Zee for some tidbits that are really neat but the book is unsatisfying. I think it's because when he covers stuff that one is interested in, the presentation is always too short to really learn anything. So one always feels "left on one's appetite" (as we say in French)

Yes. I find it interesting that the mathematician Roger Penrose in his Road to Reality (saw in another thread that you read and liked this brilliant book) referred to Zee's book more than a dozen times.

I also like Gross (it's not David Gross..I don't remember the exact title).

I have seen it. Another book that I should have another look at if I get a chance.

And Weinberg (vol 1).

Well, one can't mention QFT books without mentioning Weinberg. I like that, near the beginning, he talks about infinite-dimensional representations of the Poincare group.

I used to dislike Itzykson and Zuber but with a more solid background, I go back and appreciate it more and more.

In grad school, I had a friend who swore by this book, but I have never really looked at it.

I never liked Kaku, however.

I have Kaku, and I, too, dislike it. However, I know a number of people who really like it, e.g., my supervisor.

I forgot Ryder! I like it as a complement (a bit like Zee but at a lower level).

Supposedly, Ryder was the text for my graduate field theory courses, but the prof never made use of it. In fact, in the second semester, he brought photocopies of a few pages from Raymond to each lecture, and transcribed these verbatim onto the board, all the while not letting on what he was doing. Raymond wasn't even on the readings list that he distributed to the class!

I sincerely hope that the 4-vector that connects the now event on my worldline to the event of me purchasing my favourite QFT book is future-directed. I don't much like the thought that this 4-vector is actually past-directed!

 

[maverick280857]

My favourite pedagogical treatments of relativity are https://www.amazon.com/gp/product/0070430276/?tag=pfamazon01-20 by James Hartle. I can't say enough good things about these books.

I did not know about Moore's book but I do refer to Hartle.

 

[samalkhaiat]

What are your favourite QFT books (at all levels).

My favourite with my rating:

BOGOLIUBOV & SHIRKOV (************** more stars might do justice)

ITZYKSON & ZUBER (******)

WEINBERG (V1) (*****)

HATFIELD (*****)

GREINER (FIELD QUANTIZATION) (****)


Regards

sam

 

[George Jones]

BOGOLIUBOV & SHIRKOV (************** more stars might do justice)

Is that the green one? Or is it purplish?

 

[nrqed]

Me too!

I would then highly recommmend buying Hatfield's book, George. The presentation is fairly original and quite thorough. And he makes some effort to discuss things at a conceptual level. He repeats several calculations three times, using canonical quantization, path integral quantization and using a wave functional approach ( I think that when a new formalism is introduced, it is very pedagogical to rederive results already known as a mean to gain familiarity with the new formalism. Unfortunately, books (and teachers) rarely do that. Hatfield is good about repeating a given calculation using different formalisms. And the string theory part is also very good!)

I am not sure that Maggiore will show you anything new, but I hope you like it.

That's ok. What I want is to see fresh presentations and explanations in order to get a deeper understanding. I don't mind if I don't learn anything new in terms of actual formalism or calculations.

By the way, I have ordered Greiner also (Field quantization) and will let you know how I find it.

I particularly like Ticciati's treatment of symmetries in chapters 3, 6, 14, 15, and 16. He take a little more mathematical care than does a typical QFT book, but I don't think that he takes so much care that physicists will be completely turned off.

That sounds very interesting. It's unfortunate that it is so expensive :-(

Again, I have similar feelings. I was quite sure that you felt this way, so this is one reason that I am interested in your opinions on QFT books.



I don't really know enough to comment, but maybe this is relevant. If A and B are self-adjoint operators, then [A , B] =0 ==> [f(A) , f(B)] = 0 for nice functions f and g. Maybe P&S want to apply this to (not necessarily self-adjoint) field operators, so that measurements of obervables built from field observables (via the functions f and g) are guaranteed not affect each other.

That is exactly right. Thanks for reinforcing my interpretation. I have realized that this is the key point. Since observables are constructed out of the fields, the vanishing of their commutator at spacelike separation implies causality of any measurement, even though the Phi's themselves are not observables.

But you see what I mean...to *me* this specific point (which requires only a few sentences to address) is *key* in understanding the whole issue of causality. And yet it is not explained at all in P&S! (which is meant to be fairly pedagogical). This is what annoys me about QFT books. It feels like the physical interpretation is neglected very badly. Books end up manipulating operators and states and other expressions for pages and pages without ever stopping to discuss what they represent (are these operators observables? is this quantity an amplitude for finding a particle at one position? Is that a measurable quantity? And on and on)

So do I, and I like Halzen and Martin.

I do too, I did not mention it because I did not get into Particle Physics books (Granted, Griffiths is really a particle physics book, not a QFT book. But I think undergrads should be introduced to the applications of QFT and to some Feynman diagram calculations before plunging into QFT)

I don't have this, but I am thinking of ordering the new 2-volume edition of Aitchison and Hey.

I have to check this, I did not know they had a two volume edition! (what I have is quite old, maybe there is a lot of new stuff that I would enjoy reading).

I think Gauge Theories of Particle Physics is *excellent*. It *is* very basic though, but what is covered is presented in a very pedagogical way.
That's the only book where I have seen a discussion of "old fashioned perturbation theory" (also called "time-ordered perturbation theory") which shows clearly the connection between the language of covariant perturbation theory of Feynman diagrams with the perturbation theory of quantum mechanics (the latter involving several time-orderd diagrams - the so-called "Z" graphs - with particles propagating backward in time which are recovered by doing the sum over the poles of the covariant expression.)

Friday afternoon I downloaded a copy of Aitchison's long pedagogical article "Nothing's plenty: The vacuum in modern quantum field theory," Contemporary Physics, 26(4), 1985. I haven't had a chance to take a look at it yet.

Is it available for free?

Yes. I find it interesting that the mathematician Roger Penrose in his Road to Reality (saw in another thread that you read and liked this brilliant book) referred to Zee's book more than a dozen times.

Btw, I *LOVE* Penrose's book! It is so refreshing to see such an incredible range of concepts discussed almost completely at the conceptual level. It is a brilliant book! I don't know how many times I have read something and felt like a light bulb just lit up in my head!

Well, one can't mention QFT books without mentioning Weinberg. I like that, near the beginning, he talks about infinite-dimensional representations of the Poincare group.

I need to go back and look at it in more details. I felt that it was getting a bit too heavy at some point and I needed a break.
I liked that he used as a starting point the need to have a theory allowing for a changing number of particles and that this *leads* to the idea of a quantum field. As opposed to everyone else who start by saying "we must now consider classical fields and quantize them" without explaining where the heck this comes from! I always disliked that. What is a classical Dirac field anyway? It is totally weird to me that one would find natural to introduce the idea of QFT by saying that we need to quantize all those classical fields that have no observational basis. Even if the Higgs exists, what the heck would be the classical Higgs field?

I have Kaku, and I, too, dislike it. However, I know a number of people who really like it, e.g., my supervisor.

yes?! That surprises me.

Supposedly, Ryder was the text for my graduate field theory courses, but the prof never made use of it. In fact, in the second semester, he brought photocopies of a few pages from Raymond to each lecture, and transcribed these verbatim onto the board, all the while not letting on what he was doing. Raymond wasn't even on the readings list that he distributed to the class!

I had forgotten about Raymond. I bought it and tried to read it when I was just beginning to learn QFT. And I disliked it. Maybe now I would appreciate it more. I should dig it out of my library.

I sincerely hope that the 4-vector that connects the now event on my worldline to the event of me purchasing my favourite QFT book is future-directed. I don't much like the thought that this 4-vector is actually past-directed!

lol!

Well, maybe *you* should write it!

I wish there was a book on QFT at the level of Wheeler and Taylor's book
"The physics of Black holes". Something intermediary between the little QFT of Griffiths and P&S.



Thank you for your comments, they are much appreciated.

Regards

Patrick

 

[Ratzinger]

I bought the Maggiore book one week ago and like it very much. As many others I find QFT extremely difficult to learn and kept searching for a good introductory text. I think this one good be it. It is extremely well structured, very compact, has solved problems and feels modern.



Hi Pertubation

What!? You are sixteen and reading and understanding Peskin/ Schroeder? That makes me extremely jealous. What are you doing when you are twenty-three? I'm jealous.


Hi nrqed

I remember you are learning python, here is a link to a book site of the coolest book ever written (http://www.physics.cornell.edu/sethna/StatMech/) . It is about statistical mechanics and happens to be from the same Oxford series that also the Maggiore book is from. But the book is not only exciting, thrilling and lots of fun, the author is also a nice person, so that he puts the book free on the net and programs for its computer models with codes in phyton.

 

[nrqed]

I bought the Maggiore book one week ago and like it very much. As many others I find QFT extremely difficult to learn and kept searching for a good introductory text. I think this one good be it. It is extremely well structured, very compact, has solved problems and feels modern.

Hi Ratzinger. I would love to hear any comment or suggestion you have about other QFT books!

Hi nrqed

I remember you are learning python, here is a link to a book site of the coolest book ever written (http://www.physics.cornell.edu/sethna/StatMech/) . It is about statistical mechanics and happens to be from the same Oxford series that also the Maggiore book is from. But the book is not only exciting, thrilling and lots of fun, the author is also a nice person, so that he puts the book free on the net and programs for its computer models with codes in phyton.

He is indeed a nice person (I know him from my days at Cornell).
I did not know about his book and the programs. Thank you very much!

(while we are talking about Stat Mech stuff, one of my favorite physics books in terms of pedagogy and clarity is The Theory of Critical Phenomena: An introduction to the Renormalization Group by Binney, Dowrick, Fisher and Newman, also in the Oxford series. The authors do a remarkable job at *explaining* things very pedagogically. Actually, it has a lot of relevance to QFT so I should have put it in my list!)

Patrick

 

[Perturbation]

Hi Pertubation

What!? You are sixteen and reading and understanding Peskin/ Schroeder? That makes me extremely jealous. What are you doing when you are twenty-three? I'm jealous.

I was kind of forced into it, not that I resent it. Education over here sucks, in my opinion. It started with calculus in year 10 after getting incredibly bored and now I'm where I am. I'm not getting anything out of it qualification wise, just a head start before I go to uni' next year and the "pleasure of finding things out".

 

[samalkhaiat]

Is that the green one? Or is it purplish?

How embarrassing, I have been using the book for nearly 10 years yet I could not remember its colour! I was :zzz: :zzz: all these years.
Looking at it now I can tell you, it is creamish. It is the 1980 edition.

BOBOLIUBOV, wrote 2 books on QFT. The one I like very very much is written with SHIRKOV, and it is called;
"INTRODUCTION TO THE THEORY OF QUANTIZED FIELDS"
VIII of the "INTERSCIENCE MONOGRAPHS IN PHYSICS & ASTRONOMY"

The second book was written with LOGUNOV & TODROV, This one called
"INTRODUCTION TO AXIOMATIC QUANTUM FIELD THEORY", 1975 English edition, I think this is the green one.

regards

sam

 

[maverick280857]

I was kind of forced into it, not that I resent it. Education over here sucks, in my opinion. It started with calculus in year 10 after getting incredibly bored and now I'm where I am. I'm not getting anything out of it qualification wise, just a head start before I go to uni' next year and the "pleasure of finding things out".

Perturbation, which part of the world are you from? I am entering the first year of college and doing a lot of self-reading too, which is fun.

 

[maverick280857]

By the way, isn't Griffiths' Elementary Particles (for particle physics related QFT) to be read before a formal introduction to QFT?

 

[nrqed]

By the way, isn't Griffiths' Elementary Particles (for particle physics related QFT) to be read before a formal introduction to QFT?

Yes, absolutely.
It's a wonderful book, imho. I think that pedagogically it is much better to teach a bit about Feynman diagrams and their use *before* showing how to derive them from QFT.

Patrick

 

[Cexy]

I certainly wish that I'd read about Feynman diagrams and had seen how to make use of them before being given the (very formal) introduction that I had in my undergraduate QFT course. I think that the course that my Physicist friends followed might have been the best one, where all of the concepts were introduced at a much lower level than in my course (Mathematics) so they knew more, but didn't know it as rigorously. They were then able to switch to the Mathematics course for the fourth year and get a rigorous foundation for all the stuff they'd been learning.

As far as basic introductions to QFT go, I'd recommend Peskin & Schroeder. It starts at a very easy pace and covers everything as fully as you'd want for a first course. However, for some more advanced topics (solitons spring to mind, and to some extent the standard model) I'd recommend taking a look at Kaku. Many people seem to dislike it but I've foudn it very useful as I prepare to start my PhD next year.

Take all this with a pinch of salt - I've only just finished my undergrad, and there are many people on here with more experience than me!

Chris

 

[Perturbation]

Perturbation, which part of the world are you from? I am entering the first year of college and doing a lot of self-reading too, which is fun.

The UK, north east.

 

[George Jones]

I would then highly recommmend buying Hatfield's book, George. The presentation is fairly original and quite thorough.

Thanks - I have seen positive comments about this book by other people as well.

But you see what I mean...to *me* this specific point (which requires only a few sentences to address) is *key* in understanding the whole issue of causality. And yet it is not explained at all in P&S! (which is meant to be fairly pedagogical). This is what annoys me about QFT books. It feels like the physical interpretation is neglected very badly. Books end up manipulating operators and states and other expressions for pages and pages without ever stopping to discuss what they represent (are these operators observables? is this quantity an amplitude for finding a particle at one position? Is that a measurable quantity? And on and on)

When students first see quantum field theory, they often conflate fields and states - I know I did.

I think Gauge Theories of Particle Physics is *excellent*. It *is* very basic though, but what is covered is presented in a very pedagogical way.

I am fairly sure that I will order this.

That's the only book where I have seen a discussion of "old fashioned perturbation theory" (also called "time-ordered perturbation theory") which shows clearly the connection between the language of covariant perturbation theory of Feynman diagrams with the perturbation theory of quantum mechanics (the latter involving several time-orderd diagrams - the so-called "Z" graphs - with particles propagating backward in time which are recovered by doing the sum over the poles of the covariant expression.)

After reading this, I half remembered reading elsewhere that Bjorken and Drell does something like this, but I could be completely wrong. When I was a beginning grad student, I bought the wrong Bjorken and Drell.

Is it available for free?

Can you download it from your library?

Btw, I *LOVE* Penrose's book! It is so refreshing to see such an incredible range of concepts discussed almost completely at the conceptual level. It is a brilliant book! I don't know how many times I have read something and felt like a light bulb just lit up in my head!

Yes, I love it too - probably one on my desert island books.

I liked that he used as a starting point the need to have a theory allowing for a changing number of particles and that this *leads* to the idea of a quantum field. As opposed to everyone else who start by saying "we must now consider classical fields and quantize them" without explaining where the heck this comes from!

Again, you have reminded me of something. A while ago I looked at the relationship between the formalism for a variable number of particles and the formalism for quantizing a field. This is Wald's field theory book, and I tried to come up with a more readable (at least for me!) version of Wald wrote. Another thing I should go back and look at.

I always disliked that. What is a classical Dirac field anyway? It is totally weird to me that one would find natural to introduce the idea of QFT by saying that we need to quantize all those classical fields that have no observational basis. Even if the Higgs exists, what the heck would be the classical Higgs field?

I understand what you're saying. I guess we see (some boson) classsical fields, which we realize need to be quantized. We then see that a similar formalism then gives us fermionic quantum fields, but these don't have a classical limit. It never quite clear when one should take a positivist's viewpoint, and when one should ask for deeper reasons.

yes?! That surprises me.

Could you clarify this a bit. Are you surprised that

1) I don't like Kaku
2) other people, including my supervisor, do like Kaku

or both?

I wish there was a book on QFT at the level of Wheeler and Taylor's book "The physics of Black holes". Something intermediary between the little QFT of Griffiths and P&S.

I very much like this book and have been through much of it line by line. The stuff I learned in this book (with a bit of help from Hartle as well) allowed me to write a Java applet for orbits of particles around black holes.

I do have a couple of minor criticisms, though. I found 3.3 (variational principle in words) to be confusing, and I think the (metre stick) analysis on page B-8 makes it seem that, even inside the event horizon, r is a spatial coordinate.

Thank you for your comments, they are much appreciated.

As are yours. Sorry about the long delay in replying. I do find this thread to be very interesting.

 

[maverick280857]

Hi nrqed

I remember you are learning python, here is a link to a book site of the coolest book ever written (http://www.physics.cornell.edu/sethna/StatMech/) . It is about statistical mechanics and happens to be from the same Oxford series that also the Maggiore book is from. But the book is not only exciting, thrilling and lots of fun, the author is also a nice person, so that he puts the book free on the net and programs for its computer models with codes in phyton.

The statmech link won't work...

 

[maverick280857]

The discussions here are quite interesting though I must admit that I am still learning QM so I have no idea of QFT and the QED-related ideas I know are from Feynman's book and another very nice book called "QED: The Jewel of Physics" by Dr. G Venkataraman (Universities Press, India). After Feynman's book, this series is the best set of books for any school going student or anyone introduced to basic calculus and physics. It describes many ideas like Feynman diagrams, scattering and perturbation theory in a lucid manner. In fact I think this book should be read by even the serious physics students getting into QFT/QED related areas.

Also, I thought it would be a good idea if all you QFT/QED guys/string theorists on PF would get together and write up about the prerequisite theortical physics and mathematics topics that are stepping stones to understanding things like quantum field theory, quantum electrodynamics, quantum chromodynamics, string theory, loop quantum gravity, etc. This would be useful for both physics students to get them interested in what they are doing at the undergrad level and also for people like me who want to do something in physics but do not have any first-hand experience of coursework. Finally, it would be of a lot of use to people getting into physics grad school especially from branches other than physics. What do you think?

 

[Perturbation]

That's not a bad idea if it doesn't already exist...anyone else?

 

[selfAdjoint]

The statmech link won't work...

Here is Professor Sethna's home page http://www.lassp.cornell.edu/sethna/sethna.html

but I don't know if the stat mech book shown there as coming out "in April" is the one referred to by Ratzinger.

 

[maverick280857]

Thanks. I'll check it out.

 

[nrqed]

Thanks - I have seen positive comments about this book by other people as well.



After reading this, I half remembered reading elsewhere that Bjorken and Drell does something like this, but I could be completely wrong. When I was a beginning grad student, I bought the wrong Bjorken and Drell.

Lol!

Now that you mention it, I *think* that I remember seeing old-fashioned perturbation theory in Bjorken and Drell, yes. In the "old days" it was much better known. In another thread, when I mentioned old-fashioned perturbation theory I was basically called a crackpot by someone who has an advanced degree in particle physics!

Yes, I love it too - probably one on my desert island books.

Lol! My thought exactly! I would want to have Penrose's book around on a desert island.

Again, you have reminded me of something. A while ago I looked at the relationship between the formalism for a variable number of particles and the formalism for quantizing a field. This is Wald's field theory book, and I tried to come up with a more readable (at least for me!) version of Wald wrote. Another thing I should go back and look at.

Neat! Wald has a field theory book? Do you mean his book about QFT in curved spacetime? (I might be mixing up books or authors here).

It's funny that you are mentioning this because I am trying to come up with a more readable (for me!) introduction to QFT based on Weinberg's approach and its connection with the standard "quantizing a classical field theory" approach.

I understand what you're saying. I guess we see (some boson) classsical fields, which we realize need to be quantized. We then see that a similar formalism then gives us fermionic quantum fields, but these don't have a classical limit. It never quite clear when one should take a positivist's viewpoint, and when one should ask for deeper reasons.

Indeed. However, in Weinberg's approach the starting point is that we need to allow the number of particles to vary (because of relativity). Then everything else follows! Quantum fields, their CRs, etc. I find it much more satisfying to use this as a starting point than to start with those unobservable classical fields!

Could you clarify this a bit. Are you surprised that

1) I don't like Kaku
2) other people, including my supervisor, do like Kaku

or both?

Sorry, my statement was really unclear! I meant to say that I was surprised that other people like Kaku!
I still look at his superstring theory book now and then and find it so weird. It feels like now and then there are tidbits of very useful and insightful comments but they are lost in the middle of mostly incomprehensible stuff. As if he had a genuine desire to be pedagogical for brief sections and then he decides to go through a lot of stuff quickly iwthout worrying if it is understandable for the uninitated.

I very much like this book and have been through much of it line by line. The stuff I learned in this book (with a bit of help from Hartle as well) allowed me to write a Java applet for orbits of particles around black holes.

I do have a couple of minor criticisms, though. I found 3.3 (variational principle in words) to be confusing, and I think the (metre stick) analysis on page B-8 makes it seem that, even inside the event horizon, r is a spatial coordinate.

I will look at these sections with your comments in mind!

As are yours. Sorry about the long delay in replying. I do find this thread to be very interesting.

No need to apologize. I am sorry too for having taken so long ot reply, however

It is indeed very interesting!

Patrick

 

[PRB147]

I think quantum mechanics and Relativistic kinetics is enough for your study in QED. As to Group theory, I think that Lorentz group and Poincare group is enough. Because QED is U(1) symmetry, so the gauge structure of QED is very simple.
I recommend some books for you
1) A first book of quantum field theory, A. Lahiri, and P.B. Pal, Alpha science international LTD. 2001
2) quantum electrodynamics, V.N. Gribov, and J. Nyiri, CUP press

 

[maverick280857]

A QFT book by Mark Sredniki is available here: http://gabriel.physics.ucsb.edu/~mark/MS-QFT-11Feb06.pdf

 

[maverick280857]

I think quantum mechanics and Relativistic kinetics is enough for your study in QED. As to Group theory, I think that Lorentz group and Poincare group is enough. Because QED is U(1) symmetry, so the gauge structure of QED is very simple.
I recommend some books for you
1) A first book of quantum field theory, A. Lahiri, and P.B. Pal, Alpha science international LTD. 2001
2) quantum electrodynamics, V.N. Gribov, and J. Nyiri, CUP press

Thanks. What about Relativistic QM?

 

[nrqed]

A QFT book by Mark Sredniki is available here: http://gabriel.physics.ucsb.edu/~mark/MS-QFT-11Feb06.pdf

ANother online QFT book (293 pages!) is available here
http://www.physics.ucsd.edu/~crs/physics/research/QuantumFields-Krauss.pdf

 

[neutrino]

When you guys have time, take a look at this page
Fields and Particles Bookmarks. It's a HUGE repository of notes in QM, maths for QM and QFT.There are some C(lassical)FT links, too (mostly GR).

Btw, Geocities has been down for sometime.

 

[nrqed]

A QFT book by Mark Sredniki is available here: http://gabriel.physics.ucsb.edu/~mark/MS-QFT-11Feb06.pdf

WOW!
That's a wonderful book! Very clear and complete (615 pages!)

Thanks a lot for the link!

 

[PRB147]

Thanks. What about Relativistic QM?

According to my experience, you can start your QFT directly,
you need not to know everything.

 

[maverick280857]

According to my experience, you can start your QFT directly,
you need not to know everything.

Interesting that you say that. The QFT book (link below) says you need to know a set of equations (some from QM, electromagnetic theory, and from relativistic QM) before you can use it. I am referring to this one: http://gabriel.physics.ucsb.edu/~mar...FT-11Feb06.pdf

 

[nrqed]

Interesting that you say that. The QFT book (link below) says you need to know a set of equations (some from QM, electromagnetic theory, and from relativistic QM) before you can use it. I am referring to this one: http://gabriel.physics.ucsb.edu/~mar...FT-11Feb06.pdf

You are referring to his euqations on page 7, right?

There is no equation from "relativistic QM".
The first 4 equations are from nonrelativistic QM. The 5th one (H= p qdot -L) is classical mechanics. The next two are from special relativity (no need to introduce QM, just classical SR) and the last one is from classical electromagnetism.

Are you familiar with these?
If not, which ones are you not familiar with? Are you familiar with special relativity?

Regards

Patrick

 

[maverick280857]

Okay I am teaching myself QM from Griffiths (with occasional reference to Schiff, Powell, Eisberg/Resnick--textbook2, and anything else that I find on the net). I am about to start chapter 3 (doing problems in chapter 2) so my knowledge of "equations" is limited to what I have seen upto chapter 2 and equivalent sections from other places.

I was told by a senior student that to understand QFT I need to understand QM properly first, followed by special relativity (oh and I am still learning about four-vectors/transformations...nothing more yet) and then relativistic QM (also electromagnetic theory) So my quess was that the equations I don't know are from relativistic QM...maybe I was wrong then.

Specifically I have "seen" the first equation and probably the third. I "know" something about the second equation. What I do not know then are the first, third, fourth and fifth equations. So maybe you can point me to the topics I don't know yet (which are many )

EDIT: Okay I think I know the fifth one but not properly (the notation isn't clear to me...I have never seen this in Lagrangian/Hamiltonian but again I must've only scratched the surface.)

 

[nrqed]

Okay I am teaching myself QM from Griffiths (with occasional reference to Schiff, Powell, Eisberg/Resnick--textbook2, and anything else that I find on the net). I am about to start chapter 3 (doing problems in chapter 2) so my knowledge of "equations" is limited to what I have seen upto chapter 2 and equivalent sections from other places.

I was told by a senior student that to understand QFT I need to understand QM properly first, followed by special relativity (oh and I am still learning about four-vectors/transformations...nothing more yet) and then relativistic QM (also electromagnetic theory) So my quess was that the equations I don't know are from relativistic QM...maybe I was wrong then.

Special relativity is quite independent from quantum mechanics. If you see equations from relativity, they are from "classical" relativity, they have nothing to do with QM per se. "relativistic QM" is, strictly speaking nothing else than QFT!

Specifically I have "seen" the first equation and probably the third. I "know" something about the second equation. What I do not know then are the first, third, fourth and fifth equations. So maybe you can point me to the topics I don't know yet (which are many )

EDIT: Okay I think I know the fifth one but not properly (the notation isn't clear to me...I have never seen this in Lagrangian/Hamiltonian but again I must've only scratched the surface.)

Hi.

You do not need to learn "relativistic QM", no. (and there is no such thing really as relativistic QM, it's really QFT !).

In Griffiths, the first eq is covered in the chapter on scattering. But you don't need this really for quite a while in QFT.
The second appears in the treatment of the harmonic oscialltor using ladder operators (VERY important for the study of QFT). The third is in the section on angular momentum.
I am not sure if Griffiths covered the 4th one. You have to look up the "Heisenberg representation" in a more complete textbook. Also very important for the study of QFT.


The fifth is really important. You need to learn and study the Hamiltonian and Lagrange approaches to classical mechanics, using Goldstein, for example.

You need to get much more familiar with special relativity too (and then the 6th and 7th equation will be well known).

And you need to develop a good basis in classical E&M too (the book by Griffiths on the subject is good too).

If you want my opinion, after learning all this stuff, before getting into a QFT book per se (like this online book), read the particle physics book by Griffiths. It would be worth your time, unless you are specifically interested in applying QFT to condensed matter only and not to particle physics.

My two cents

Patrick

 

[maverick280857]

Thanks for your two cents, Patrick

Yup loved the section on ladder operators and read it from several other places too. Still to make a formal foray into angular momentum though. And yes, I am studying electromagnetic theory from Griffiths too. I have the particle physics book by Griffiths and I think what you mean is do

Quantum Mechanics
Special Relativity
Electromagnetic Theory

and then read the Griffiths Elementary Particles book before studying QFT from anywhere else right?

No, I am interested in QFT first (and particle physics).

 

[nrqed]

Thanks for your two cents, Patrick

You are welcome

Yup loved the section on ladder operators and read it from several other places too. Still to make a formal foray into angular momentum though. And yes, I am studying electromagnetic theory from Griffiths too. I have the particle physics book by Griffiths and I think what you mean is do

Quantum Mechanics
Special Relativity
Electromagnetic Theory

yes, but don't forget "advanced" classical mechanics (Hamiltonian, Lagrangian, principle of least action, Poisson brackets). I think that you should try to get a copy of Shankar's QM book, it is quite good and gives a nice introduction to those concepts of classical mechanics. It is a very good book fro learning QM be oneself because it is both very clear and pretty self-contained.

Also make sure to see applications of the lagrangian and hamiltonian formalism to classical *fields*, not just systems of point particles. In particular study classical EM treated using the lagrangian approach (and in particular why this requires one to work with the potentials {\vec A} and \Phi instead of working with the E and B fields).

and then read the Griffiths Elementary Particles book before studying QFT from anywhere else right?

Yes, that was my suggestion.

No, I am interested in QFT first (and particle physics).

Ok. Then I think reading Griffiths' particle physics book becfore getting into a QFT textbook (like Peskin and Schroeder) is very worthwhile.

Actually, I would suggest the following:

Getting a solid basis in classical mechanics, classical E&M, QM and in relativity, then reading Griffiths's particle physics book, then reading Aitchison and Hey, and then a more advanced QFT book.

All the while posting here any question you have!
Are you planning to do all this mostly by yourself or are you going to take classes? It's always important to be able to interact with other people and to discuss things, books can never completely replace this.


Just my opinion.

Patrick

 

[maverick280857]

Are you planning to do all this mostly by yourself or are you going to take classes? It's always important to be able to interact with other people and to discuss things, books can never completely replace this.

Sure. But I most likely will be majoring in Electrical Engineering so not much advanced physics for me (as courses). But I agree with you on that one.

 

[nrqed]

Sure. But I most likely will be majoring in Electrical Engineering so not much advanced physics for me (as courses). But I agree with you on that one.

Ah! Ok! So you are interested in QFT and particle physics just for the pleasure of learning the topics?

Given your situation, you should take advantage of these forums as much as possible! And when you get to learning QFT, let me know. As I have discussed here many times I dislike the conventional presentation (which feel way too "ad hoc" for me). But we can discuss that later.

Good luck!