Prerequisites for Quantum Electrodynamics

[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!

 

[maverick280857]

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

Well I wanted to do physics, but I had to get into engineering. So the answer to your question in two words is: "not just". I want to (formally) https://www.physicsforums.com/showthread.php?t=122582" particle physics later in life if possible so I am keeping up my interests.

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!

Thank you

 

[CarlB]

It's possible to split the effort to understand elementary particles into two parts, roughly defined by internal versus external symmetries.

Of these two, the more simple, in my opinion, is the internal symmetries (less calculus). For these, the natural tool is the Measurement Algebra, which has also seen use recently in quantum statistics. The classic introduction is by Schwinger and is quite inexpensive:


Carl

 

[Hans de Vries]

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).

Griffiths is probably the best way to start in QFT. You may read in parallel
Halzen and Martin's "Quarks & Leptons", 1984 which seems to have inspired
Griffiths book from 1987 in many ways. Griffith's book follows the same
path but Halzen & Martin go a bit deeper. The both of them are a good
combination for self study.

Other good reads are Aitchinson and Hey, Volumes I and II, The third
editions are from 2002 and 2003 so they include much of the recent
experimental results. I see they are mentioned above as well.

I do like Lewis Ryder's "Quantum Field Theory" a lot.

It's good to have some feeling for the origins as well. Understanding the
historical development and knowing the people behind it. There are
many original papers in books like:

"Sources of Quantum Mechanics" B.L. van der Waerden. and
"Selected papers on Quantum Electrodynamics" Julian Schwinger.

To get to know the people there is a very entertaining book from
Martinus Veltman: Facts and Mysteries in Elementary Particle Physics.
Veltman has a technical book as well which handles the whole SM:
Diagrammatica, although it has a somewhat different notation.

And then there are of course the (technical) books from Feynman:

-The Feynman lectures on Physics, Volume III (an absolute must!)
-The Theory of Fundamental Processes
-Quantum ElectrodynamicsWell, That should be enough for the time being :^)
Regards, Hans

 

[Daverz]

http://www.oup.com/uk/catalogue/?ci=9780198520740#contents" that is at about the senior undergraduate level.

That's how it's billed. I just started reading Ch. 2 on the Lorentz and Poincare group. Maybe undergrads in the UK have more under their belt, but I think the typical undergrad in the US would be lost here without an instructor to greatly expand on the material. Ryder has a more gentle introduction.

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.

Yeah, so far it looks like a very classy production.

 

[Daverz]

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

Srerdnicki lists the following (which looks pretty messed up cut and pasted from the pdf file)

dσ/dΩ = |f(θ, φ)|^2
a†|ni = √n+1 |n+1i>
J±|j,mi = √j(j+1)−m(m±1) |j,m±1i
A(t) = e^+iHt/¯hA^e−iHt/¯h
H = pq˙ − L
ct′ = γ(ct − βx)
E = (p^2c^2 + m^2c^4)^1/2
E = − ˙A/c − ∇ϕ

Well, I tried. My translations to the relevant concepts:

Differential cross-section for scattering
The quantum harmonic oscillator and creation/annihilation operators
Angular momentum and the step-up/step-down operators
Time evolution of an operator
Halmitonian operator in QM
Lorentz transformations
4-momentum
Electric field from vector and scalar potentials.

You'd usually encounter these in the opposite order.

My undergraduate QM text, Gasiorowicz, has all of these, though it's assumed you are familiar with the vector potential and the differential forms of Maxwell's equations, and the relativity is only in an appendix; I suggest Schwartz's Principle of Electrodynamics for the E&M and Spacetime Physics for the relativity. QM is just as good a place as any to encounter the Hamiltonian for the first time, but you usually don't get the Langrangian. I'm not going to recommend Goldstein just for that, though. I have an old edition of Symon, which is a very good book, and I like his chapter on Lagrange methods, but I wonder if there's a Dover book with good coverage of this.

 

[George Jones]

That's how it's billed. I just started reading Ch. 2 on the Lorentz and Poincare group. Maybe undergrads in the UK have more under their belt, but I think the typical undergrad in the US would be lost here without an instructor to greatly expand on the material. Ryder has a more gentle introduction.

Yeah, so far it looks like a very classy production.

Yes, I agree that the material on the Lorentz and Poincare groups is quite terse. In fact, I haven't found a QFT book that treats this material the way I would like to see it treated, but I am quite biased with respect to this.

Maggiore based his book on a course he gave to senior undergrads in Switzerland, and I find that, typically, European physics students are exposed to more abstract mathematics than are North american students.