Where Can I Continue Learning QFT on My Own?

[StatusX]

I just finished an introduction to quantum mechanics class, and I was wondering where I could learn QFT on my own (including any more QM I might need to learn before I could start QFT). I have Griffiths book, and in class we covered the first 7 chapters (which includes all the basics, hydrogen, time-indep. perturbation, identical particles, and the variational principle), so I'm comfortable with this material and could learn the stuff in the rest of the book on my own. Where should I go after this?

 

[ZapperZ]

I just finished an introduction to quantum mechanics class, and I was wondering where I could learn QFT on my own (including any more QM I might need to learn before I could start QFT). I have Griffiths book, and in class we covered the first 7 chapters (which includes all the basics, hydrogen, time-indep. perturbation, identical particles, and the variational principle), so I'm comfortable with this material and could learn the stuff in the rest of the book on my own. Where should I go after this?

I would strongly suggest you wait till you have done perturbation theory and Second Quantization.

Zz.

 

[dextercioby]

What about dynamical systems with constraints...?All nonzero spin classical fields have either I-st class or second class constraints.

It's not only QM. Classical field theory,too.

Daniel.

 

[vanesch]

I just finished an introduction to quantum mechanics class, and I was wondering where I could learn QFT on my own (including any more QM I might need to learn before I could start QFT). I have Griffiths book, and in class we covered the first 7 chapters (which includes all the basics, hydrogen, time-indep. perturbation, identical particles, and the variational principle), so I'm comfortable with this material and could learn the stuff in the rest of the book on my own. Where should I go after this?

Well, you should probably first become a bit more confortable with QM. I strongly suggest you read "Modern Quantum Mechanics" by J.J. Sakurai. I know that there are other people preferring other books for quantum mechanics per se, but you have to know that Sakurai wrote this book _especially_ as a preparation for QFT afterwards.

A while ago I organized an internet course on this book, and some material from that period is still left on a website I set up for the occasion:

http://perso.wanadoo.fr/patrick.vanesch/nrqmJJ/NRQM_main_page.html

In fact the course fell on its face after the first part, because there was not much very active participation anymore. So I never got to the second part, that's why there is less material.

cheers,
Patrick.

 

[straycat]

I just finished an introduction to quantum mechanics class, and I was wondering where I could learn QFT on my own (including any more QM I might need to learn before I could start QFT). I have Griffiths book, and in class we covered the first 7 chapters (which includes all the basics, hydrogen, time-indep. perturbation, identical particles, and the variational principle), so I'm comfortable with this material and could learn the stuff in the rest of the book on my own. Where should I go after this?

Hey Status,

I'll put in my two cents as someone who has taken a basic hardcore QM class and then learned a lot more on my own over the years. By profession I'm not a physicist, so take it for what it's worth . I'd say that Feynman's Lectures on Physics, Volume III on QM, is a fantastic resource for getting a strong intuitive feel for QM, even though it's over 40 years old now. If you like Feynman's way of thinking, you could go from his Lectures to the Feynman and Hibbs text Quantum Mechanics and Integrals, which lays out the Feynman path integral formulation.

I don't know enough about QFT to know how the FPI fits into QFT. But I would also strongly recommend a very short paper by Dan Styer, "Nine formulations of quantum mechanics," Am J Physics 70(3), March 2002, p 288, that gives an overview of, well, you can guess from the title. (The FPI is one of the nine.) It may be that one of these various formulations is particularly better suited than the others as a foundation for QFT, I don't know. If you or anyone else knows, I'd be interested!

David

 

[juvenal]

I would go to the bookstore and browse Zee's Quantum Field Theory in a Nutshell, and see how much of it you can handle. Zee is a fairly new book, and has a modern approach to QFT.

Griffiths' Introduction to Elementary Particles is fairly accessible to a person who knows some QM, and covers Feynman diagrams at a very basic level. Also Halzen and Martin, which is a bit more difficult than Griffiths. Griffiths pretty much rips off Halzen and Martin, actually, but that's an issue independent of the quality of the textbook.

 

[dextercioby]

Or you can do it another way:Read Feynman & Hibbs with their Path Integral text and then go to Bailin & Love "Introduction to Gauge Field Theory",Adam Hilger,2-nd Edition,1993. It covers pretty much everything from the SM,but u need to know path integrals and why are they useful in a quantum theory.

Daniel.

 

[StarshipX]

Steven Weinberg is all one needs.

 

[juvenal]

Or you can do it another way:Read Feynman & Hibbs with their Path Integral text and then go to Bailin & Love "Introduction to Gauge Field Theory",Adam Hilger,2-nd Edition,1993. It covers pretty much everything from the SM,but u need to know path integrals and why are they useful in a quantum theory.

Daniel.

It'd be nice if they could republish Feynman and Hibbs. Costs $325 on Amazon, and all the copies in the Caltech library system are checked out.

There's a relatively book by Mosel on path integration. No reviews on Amazon though.

 

[dextercioby]

Check out #4 from this list.The .pdf files are FREE !

http://www.physik.fu-berlin.de/~kleinert/kleiner_re.html

Daniel.

 

[juvenal]

Check out #4 from this list.The .pdf files are FREE !

http://www.physik.fu-berlin.de/~kleinert/kleiner_re.html

Daniel.

Cool - but more than half of the text appears to be in German.

However, there's another one further down the list that is fully in English.

 

[StatusX]

OK, thanks for all your help so far. So what exactly do I need to learn before I'll be ready for QFT, and where can I find it? dexter, you mentioned "nonzero spin classical fields": what is that, and do I need to know it?

 

[dextercioby]

The name says it all:QFT is Quantum Field Theory.That is:the quantum theory of fields.It deals with quantized fields.So u'll have to get a grip on fields:what are they and what do they do and why do we need to quantize them...?What does quantization mean...?

"Spin" of a field:the dimension of the irreducible representation of the restricted Lorentz group.Example:the scalar field corresponds to the (0,0) representation of the restricted Lorentz group and its operator is the unit operator acting on the linear space of this representation.

That's classical field theory.What are fields & what do they do.

Daniel.

P.S.Will u be taking QFT in college,eventually,or not?

 

[straycat]

Or you can do it another way:Read Feynman & Hibbs with their Path Integral text and then go to Bailin & Love "Introduction to Gauge Field Theory",Adam Hilger,2-nd Edition,1993. It covers pretty much everything from the SM,but u need to know path integrals and why are they useful in a quantum theory.

Daniel.

I suppose you are implying that Status should focus more on the FPI than on some other formulation of QM, eg Heisenberg's matrix formulation or Schrodinger's wave mechanics, as prerequisite for QFT. Is this what you mean, and do others agree? At a conceptual level, how does the FPI lead to QFT?

David

 

[dextercioby]

Depends...I've been taught QFt both ways.In QCD and EW,the operatorial approach is useless,so why not do everything path integral...?After all,Wick's theorem looks a lot simpler playing with nonconnected Green functions,right?

Anyway,i still hope the OP will not attempt to study QFT all by himself.He needs a teacher,lecture notes,explanations and just then self-study.

My say.

Daniel.

 

[StatusX]

I'm finishing up my sophomore year now, and I'll be going on to grad school, where I presume I'll take some classes QFT. I just wanted to get started now because (a) I'm curious and interested in it and (b) I want to do research next year and I'd like to actually be useful, or at least stand out from some of the other undergrads. And by the way, I've always learned much, much better on my own out of a book than by going to class or talking to professors or other students.

 

[dextercioby]

I see your point.If "research"is your goal,then mathematics should come first.U can't understand the physics without a proper education in higher mathematics.And shouls have been clear ever since the first theoretical physics course you've ever had (if u have).

Daniel.

 

[StatusX]

OK, that's why I started this thread, because I don't know what I should be doing. What math should I learn? I've always just learned the math along with the physics as it was needed.

 

[straycat]

And by the way, I've always learned much, much better on my own out of a book than by going to class or talking to professors or other students.

Well it's not an either-or thing, of course. You should continue your formal studies AND continue your self-study. (I know you know that, but it's worth saying anyway.)

David

 

[straycat]

I want to do research next year

Do you have an idea what kind of research you're interested in? I suppose as a start: theoretical or experimental?

David

 

[StatusX]

Do you have an idea what kind of research you're interested in? I suppose as a start: theoretical or experimental?

I started a thread about this in the academic guidance forum. Down the line, I'd prefer to do pure, theoretical physics, but I don't know if I'm cut out for it, so I'd fall back on aerospace engineering. If it's possible, I'd love to do research on theoretical physics. I'm just not sure how much you need to know to do that.

 

[dextercioby]

In short,a lot.Anyway,i don't see the connection.Aerospace engineering and theoretical physics.No offense,a million miles apart.

Daniel.

 

[StatusX]

True, but I'm talking about advanced (maybe theoretical) propulsion methods for spacecraft . Either way, I want to go as deep into physics as I can. I just want a backup plan if I find out I'm not smart enough to do theoretical work for a living. By the way, right now I'm majoring in applied and engineering physics, the only major that might bridge that gap.

 

[straycat]

If it's possible, I'd love to do research on theoretical physics.

Any idea what branch of theoretical physics? This may not be a fair question since you're just in your sophomore year. QM, as well as the mathematics behind it, are hugely vast fields. I think it is fair to say that there are entire branches of both that some physicists do not know even exist.

For example: if you get into theoretical physics, and study GR as well as QM (as you better do if you're going to be a theoretician!), you might learn differential forms, or maybe even Clifford algebra/geometric algebra, as two possible alternatives to the more standardized, tensor-based approach to studying curved spacetimes.

I'd once again put in a plug for the Styer paper that I mentioned earlier. Once again, some physicists are not even aware that some of these various formulations even exist!

Here's a question for you: do you consider yourself a "physicist" or a "mathematician" first? I'm guessing the former based on what you've said earlier.

David

 

[straycat]

I just want a backup plan if I find out I'm not smart enough to do theoretical work for a living.

That's a smart plan, my man. Just don't sell yourself short too quickly.

D

 

[vanesch]

True, but I'm talking about advanced (maybe theoretical) propulsion methods for spacecraft . Either way, I want to go as deep into physics as I can. I just want a backup plan if I find out I'm not smart enough to do theoretical work for a living. By the way, right now I'm majoring in applied and engineering physics, the only major that might bridge that gap.

I did something quite similar, in fact. I always wanted to do theoretical physics, but let's say that when I was studying, the prospects in that domain were meager. It's a hard battle to try to get one of the very few permanent positions, and the battle is not purely in your own hands: it depends on your thesis adviser, department politics, what wind will blow 6 years from now etc...
My dad thought that I first had to do some "real" studies, so I did electromechanical engineering. After that, I could "go and play" if I wanted to. So after that I did my physics degree. The problem was that, given my engineering background, I could easily get into an applied physics or an experimental physics program (where I was offered the possibility of starting a PhD right away) ; theory was harder to get into (simply on paper). So I took the surest path, and did experimental stuff, while taking most of the theory courses I could get.
The problem afterwards is that with an engineering degree and a PhD in experimental physics, let's say that the job market doesn't really push you into into considering a theory postdoc career: too many nice other opportunities are open. So I made a compromise: I'm working as a research engineer on rather applied physics problems, and I like reading theory on my own. Do I regret it ? Some days, I think I might have been a great theorist :-)) Then I look in the mirror again, and well, probably I would have ended up in a more lousy situation than I'm in right now (can't complain). After all, a correct income and some "job security" are things that get appreciated more over the years.
What I can say, however, is that my playing around in theoretical stuff makes the problems I'm working on for a living look very easy! It doesn't replace labwork, but where I see many of my collegues spend weeks and weeks in the lab to find out rather elementary results, it takes me half a day to work it out on a computer, and another day to check a few points in the lab. Which then leaves me some time to spend in the library, reading some interesting stuff :-)

cheers,
Patrick.

 

[NEOclassic]

Gentlemen,
IMO, the quantum field is intrinsically broadcast by electrostatic radiation from within the nucleus of all atoms including the hydrogen atom whose radiant electrostatic field is manifested in the Lyman-Balmer etc series. With the Helium nucleus, the 1s orbit begins and is different from all other "s" orbits in that its momentum increases (relative to the traditional unitary Planck unit) systematically as a function of "Z". This phenomenon has been experimentally determined for decades; yet this fact has never been addressed in all the books I have studied including Feynman's Lectures, Weinberg, Bohm, Einstein, Bohr, Gell-Mann etc. Doesn't this absence from QM field behavior make it seem that Bohm's Hidden Variable concept is real? Another unexplained variable that is due to the nature of the quantum field is how that field is able to control the order and details of the distinct difference between the 2-electron planar "s" orbits and the 6-electron "p" spherical orbitals. It is really problematic for me to understand what the heck "line integrals" might have to do with quantum field behavior. Cheers, Jim

 

[juvenal]

Gentlemen,
IMO, the quantum field is intrinsically broadcast by electrostatic radiation from within the nucleus of all atoms including the hydrogen atom whose radiant electrostatic field is manifested in the Lyman-Balmer etc series. With the Helium nucleus, the 1s orbit begins and is different from all other "s" orbits in that its momentum increases (relative to the traditional unitary Planck unit) systematically as a function of "Z". This phenomenon has been experimentally determined for decades; yet this fact has never been addressed in all the books I have studied including Feynman's Lectures, Weinberg, Bohm, Einstein, Bohr, Gell-Mann etc. Doesn't this absence from QM field behavior make it seem that Bohm's Hidden Variable concept is real? Another unexplained variable that is due to the nature of the quantum field is how that field is able to control the order and details of the distinct difference between the 2-electron planar "s" orbits and the 6-electron "p" spherical orbitals. It is really problematic for me to understand what the heck "line integrals" might have to do with quantum field behavior. Cheers, Jim

This seems so misguided that I don't even know where to begin.

 

[dextercioby]

The study of Feynman,Bohm,Gell-Mann really cracks me up...

Daniel.

 

[aav]

OK, that's why I started this thread, because I don't know what I should be doing. What math should I learn? I've always just learned the math along with the physics as it was needed.

I found this thread very helpful and interesting since I'll be starting on QFT myself in the next few weeks, and I found myself reviewing a lot of stuff. I don't have Zee, so I'll probably be using Schroeder and Peskin (and probably dipping into Bjorken and Drell). I found an eBook on QFT by Warren Siegel, where, among other things, he helpfully lists down some QFT prerequisites:

(1) Classical mechanics: Hamiltonians, Lagrangians, actions; Lorentz transformations;Poisson brackets

(2) Classical electrodynamics: Lagrangian for electromagnetism; Lorentz transformations for electromagnetic fields, 4-vector potential, 4-vector Lorentz force law; Green functions

(3) Quantum mechanics: coupling to electromagnetism; spin, SU(2), symmetries; Green functions for Schrodinger equation; Hilbert space, commutators, Heisenberg and Schrodinger pictures; creation and annihilation operators, statistics (bosons and fermions); JWKB expansion

Hope it helps people in the same situation.

 

[dextercioby]

No wonder Siegel's book is still free.It's not a textbook and is not aimed at rookies.

Zee's book is excellent in giving explanations to thorny subjects.Peskin & Schroeder is more towards a textbook,though.It would be excellent,if u had them both.

Daniel.

 

[marlon]

No wonder Siegel's book is still free.It's not a textbook and is not aimed at rookies.

Zee's book is excellent in giving explanations to thorny subjects.Peskin & Schroeder is more towards a textbook,though.It would be excellent,if u had them both.

Daniel.

I second that

marlon

 

[werty]

Ive seen requirements to take relativistic qm before qft, what do you guys think of that ? Any more links to free books covering relativistic qm dextercioby ?

 

[Miserable]

If you've studied the quantum mechanical harmonic oscillator (creation and annihilation operators), and the Lagrangian/ Hamiltonian formulation of classical mechanics, you'll be able to understand cannonical (operator-based) QFT. A lot of QFT textbooks revise the Lagrangian mechanics stuff in one of the early chapters anyway, so even that might not be too important.

If you just want an introduction, get Ryder and read the first 4 chapters (that's how I started). If you want more than that, you'll probably find it very tough going from books alone. I wouldn't start out with the path integral approach, it's much less physically intuitive.

 

[dextercioby]

Check out MIT's graduate courses on QM http://ocw.mit.edu/OcwWeb/Physics/8-322Quantum-Theory-IISpring2003/LectureNotes/index.htm

Daniel.

 

[vanesch]

Ive seen requirements to take relativistic qm before qft

Well, can somebody explain me what that IS, relativistic QM ? (and not quantum field theory!)

cheers,
Patrick.

 

[dextercioby]

Dirac's original 1928 theory.4-component wavefunction...That famous chapter in Messiah's book for example.Or Davydov's.

Daniel.

 

[vanesch]

Dirac's original 1928 theory.4-component wavefunction...That famous chapter in Messiah's book for example.Or Davydov's.

Or the first book of Bjorken and Drell... but does it still make sense to study that ?

 

[dextercioby]

Of course.QED brings refinements to Dirac's theory of H atom,but still Gordan-Fock's formula is the one to count on.

It's not fair to jump from Balmer's formula to vacuum polarization correction to 2s and 2 p levels...

And if u add the \frac{v^{2}}{c^{2}} approximation,Pauli's hamiltonian and the rigurous deduction of the terms one uses in perturbation theory...

There are reasons to still study Dirac's theory.

Daniel.

 

[baka]

Hi, I'm planning to buy some of QFT books.
Peskin would be my first choice. But I don't think that would be enough for me. Which one do u think will be better for accompany it?
Zee or Bailin&Love or Michio Kaku?

Btw anyone know any good classical field book as well? Cause I'm going to learn both subjects at the same time.

Thanks

 

[Haelfix]

Zee's book is something you can read start to finish on an airplane or something. It bypasses a lot of nitty gritty details and just outputs results, and does it in a very clear fashion. It leaves you wanting more at the end, a lot of it is just seemingly pulled out of the air, and you might be mistaken into thinking QFT is an easy subject.

Its great though as you familiarize yourself with the lingo, the notation and the equations as well as getting some good intuitive idea of how things come about.

Peskins book is also good, especially if you plan on actually using QFT a lot and problem solving with it as many calculations are painfully gone through step by step.

But in the end, Weinbergs texts are in my mind is the most complete (and hardest at the lvl of physics rigour) out there (there are harder/more complete versions available for mathematicians and theorists). When you have graduated the first 2 intro classes on QFT, read that text to see what you've been missing =)

When I first took a class in QFT in grad school, we had Zubert's.. Also a nice text, if slightly dated.

 

[aav]

Btw anyone know any good classical field book as well? Cause I'm going to learn both subjects at the same time.

I'm using Goldstein (2nd ed) to review classical field theory. It seems to work for me. The last chapter discusses the Lagrangian and Hamiltonian formulation of fields, the stress-energy tensor, gives several examples of classical fields (relativistic and non-) and ends with Noether's theorem.

 

[marlon]

Zee's book is something you can read start to finish on an airplane or something.

i always hear people saying that. This is a whole lot of crap though.

i challenge everyone to ead this book up side down or whatever and then prove me that they actually understood its content.

No Haelfix, even you studied this very thouroughly for the first time...

These words are just a manifestation of personal over estimation...

It leaves you wanting more at the end,

that is its best quality

a lot of it is just seemingly pulled out of the air,

i disagree, give some examples

and you might be mistaken into thinking QFT is an easy subject.

isn't this a bit ironic ?

marlon

 

[Haelfix]

Well like I said I already knew QFT when I studied Zee's book, so I might be biased.

But I mean look he kinda just throws it at you.. Boom here is the path integral. Here is the Chern Simmons action. This is Noethers theorem. You kinda want to see where some of the motivation is to find these things in the first place. I love his book, I truly do, but it *is* easy reading IMO, at least compared to the other texts out there.

On the complete opposite end of the spectrum is Weinberg. Everyonce and awhile I'll have to look something up , and of course I turn to his book very often (usually in volume3). Except each time I have to remind myself wth all those indices mean and where they came from, and how to get rid of them as soon as possible.

 

[juvenal]

I agree with Marlon that Zee's book is not as easy as Haelfix is making it out to be, especially since the recommendation is for a person starting out in QFT. There are exercises to do in it, after all.

 

[vanesch]

i always hear people saying that. This is a whole lot of crap though.
i challenge everyone to ead this book up side down or whatever and then prove me that they actually understood its content.

Well, I did read it in about 1 1/2 day (and a headache) from cover to cover. I do not claim having understood all of it, but I had the impression, when reading it, that I more or less didn't loose completely the thread of it. This might be mainly an illusion of course, but it didn't stop me reading. In other books, from a certain point on, you have to say that you have now read at least 5 sentences of which you didn't understand a word. That's not true for Zee.

cheers,
patrick.

 

[marlon]

Well like I said I already knew QFT when I studied Zee's book,

so did i. i had already completed my master thesis on quark confinement and the dual abelian higgs model.

But I mean look he kinda just throws it at you.. Boom here is the path integral.

i don't think you read it carefully. he explains this concept along with the mattress model in the very first chapters...he also explains why we use Noether's theorem...

i disagree with the other examples as well, sorry.

regards
marlon

ps we should not even be discussing Weinberg when considereing the very title of this thread

 

[marlon]

Well, I did read it in about 1 1/2 day (and a headache) from cover to cover. I do not claim having understood all of it,

ofcourse you did not.

[/quote]

but I had the impression, when reading it, that I more or less didn't loose completely the thread of it.

i really don't think it is possible/usefull to have an impression of what QFT is about. I mean,, i don't know if you studied it at college but i did and it was the hardest course i ever had to study...it takes several years before you actually can do something useful with QFT, even doing a masters thesis included. So i really have a hard time believing what you say, unless you inveted this theory of QFT to some extent.

In other books, from a certain point on, you have to say that you have now read at least 5 sentences of which you didn't understand a word. That's not true for Zee.

cheers,
patrick.

certainly the truth here. many people (students at colleges) think they know QM or QFT until you start asking questions like :

1) why we use quantum fields ? what is the quantum and the field part about ?
2) what is the canonical formalism ? What does canonical mean ?
3) what is the difference beween dynamical mass generation and the Higgs-related mass generation ?
4) what are dynamical quarks?
5) why do we use duality transforms?
6) what are virtual particles and what conservation laws do they respect/violate
7) what are instantons ?
8) what is asymptotic freedom ?
9) what is the path integral formalism about ?
10) give the biggest conceptual differences between QFT and QM
11) how does the Yang Mills field theories generally work
12) why eight gluons ?
13) how does symmetry account for the existence of gauge bosons ?
14) why no gauge fermions ?

etc etc

answer me to these questions and you know your basic QFT

marlon

 

[vanesch]

i really don't think it is possible/usefull to have an impression of what QFT is about. I mean,, i don't know if you studied it at college but i did and it was the hardest course i ever had to study...

Indeed, I had an (extremely bad) QFT course at university - which was not also very hard but also very confusing, and afterwards I studied Peskin and Schroeder up to a certain point myself (with the help of some internet discussions). Only after that, I read Zee, so it was indeed with some hindsight, but it DID give a view that gave more insight, in certain respects, than the more technical treatments like P&S (where sometimes you're so much burried in the calculational aspects that you loose view on the overall picture).

it takes several years before you actually can do something useful with QFT, even doing a masters thesis included. So i really have a hard time believing what you say, unless you inveted this theory of QFT to some extent.

I am not claiming that after reading Zee, you "know" QFT. But you probably get a better flavor of the subject which can then motivate you more to really delve into the matter in a more technical way.

1) why we use quantum fields ? what is the quantum and the field part about ?

I think I know.

2) what is the canonical formalism ? What does canonical mean ?

I think I know.

3) what is the difference beween dynamical mass generation and the Higgs-related mass generation ?

I think I know

4) what are dynamical quarks?

No idea.

5) why do we use duality transforms?

No idea.

6) what are virtual particles and what conservation laws do they respect/violate

I think I know

7) what are instantons ?

I have some idea.

8) what is asymptotic freedom ?

I think I know.

9) what is the path integral formalism about ?

I think I know

10) give the biggest conceptual differences between QFT and QM

That's a strange question, unless you mean by QM "non-relativistic quantum mechanics".

11) how does the Yang Mills field theories generally work

I think I know

12) why eight gluons ?

I think I know.

13) how does symmetry account for the existence of gauge bosons ?

I think I know.

14) why no gauge fermions ?

I thought I knew, and the discussion here made me see that it is not so evident :-)

From the top of my head, I think many of these questions get a BETTER intuitive answer (true, some technical stuff is hidden) in Zee than in most more calculationally oriented publications.
True, Zee doesn't justify his stuff, and you are probably not up and running to calculate much stuff yourself. But I think nevertheless that it is a great primer.

cheers,
Patrick.

 

[Kruger]

@vanesh: You should know that as scinece advisor :)