I want to learn quantum field theory. My highest education is most of QM and GR, but I'm still grasping some of the finer points of both. Is QFT "next?" I'd really like to understand QCD..

Can anyone provide any good references to sites/books/papers/magical shamans?

- Warren

here (http://arxiv.org/abs/hep-th/9912205) is a free online textbook that Tom2 recommended. he is trying to get people to get through the book over at physicsforums.com. he invited me to join that thread. except that site is down, so i don t know what s going on with that.

maybe we could make such a thread here...?

i m plugging my way through QFT on my own, right now too, so lemme see what books i can recommend. the textbook my uni uses is peskin and schroeder, which leans towards particle phenomenology and calculations. i found the book pretty hard to read, i don t really recommend it for self-study.

i m about 100 pages into siegel. i m not sure how it stacks up, but its free at least. i think i like it better than peskin + schroeder.

so apparently, s. coleman had a very famous course at harvard in QFT, and that there exists a set of his lecture notes, written up all nice, that are in common circulation in the boston area. they were highly recommended to me by our string theory prof, but i have been unable to get a copy. i think i can get my hands on one though.

i did get a copy of a book by ticciati, QFT for mathematicians. it is based on coleman s lectures, but it was written by a mathematician, so it leans heavily towards axiomatic and logical foundations considerations. it s probably not the easiest way for the beginner to learn the subject, but i m enjoying it fairly well. mathematical justifications work better on me than physical or phenomenological. and what can i say, i m a glutton for punishment.

Shazam, lethe, you're becoming my own personal Jesus Christ. Thanks a million!

- Warren

Yeah, right after I invite lethe over to my thread at PF, that site gets kicked off its server. Bummer. The admin is trying to get it working again ASAP.

We hadn't made much progress (we were going through sections 1.2 and 1.3, on Fermions and Lie Algebra) when the site went down. I have been typing up my notes on MS Word, with derivations of the equations and solutions to the exercises, and emailing them to everyone who signed up. Since this forum has an attachment feature, I could just do that instead.

So, you guys want to try going through that book here at sciforums?

Tom

I think it would be great to get some real physics going on in here. :)

- Warren

Originally posted by chroot
I think it would be great to get some real physics going on in here. :)

- Warren

I agree, but good luck with chroot around;) :D

Originally posted by Tom2
Yeah, right after I invite lethe over to my thread at PF, that site gets kicked off its server. Bummer. The admin is trying to get it working again ASAP.

We hadn't made much progress (we were going through sections 1.2 and 1.3, on Fermions and Lie Algebra) when the site went down. I have been typing up my notes on MS Word, with derivations of the equations and solutions to the exercises, and emailing them to everyone who signed up. Since this forum has an attachment feature, I could just do that instead.

So, you guys want to try going through that book here at sciforums?

Tom

yeah, tom, i m interested. physicsforums seemed like it had more physics going on, although i have to say i wasn t a big fan of the site software. but whatever. i ll go post on that thread if the site goes back up, since you ve already put some effort into it. but failing that, i wouldn t mind having some here.

btw, i think have some thoughts about that whole semi-classical limit business. i was just waiting for the site to go back up, so i could reread what you had said about it.

One thing about this book is that it is very sparse with details. I found myself having to look at a lot of other documents in order to get what Siegel is saying. A few of the references are in the attached document, which contains my notes on the first section: Nonrelativity (Galilean group, correspondence principle and so forth). I included some discussion questions, some of which I know the answers to, some I don't.

This book was written with a view to string theory, and indeed Siegel has a trilogy of books:

Fields
Superspace
Introduction to String Field Theory

I mean to go through them all. My humble research is in effective field theories for nucleon resonances, so this is meant to be an upgrading of my skills. I know QFT at the level of Sakurai (Advanced Quantum Mechanics) and Bjorken and Drell (RQM/RQF). This book is more sophisticated than that, but lacks the detailed instructions on how to do calculations. I have some online QFT notes that focus more on the "nitty gritty" of calculations, more in the spirit of Sakurai and B+D. I will probably want to supplement this thread with those notes.

OK, this forum won't let me attach MS Word files. I guess you'll have to PM your email addresses to me if you want my notes.

Tom

Originally posted by Tom2
OK, this forum won't let me attach MS Word files. I guess you'll have to PM your email addresses to me if you want my notes. I'd be interested in reading this... and I have room to host it if the author doesn't mind.

Persol@nonimitation.net

Hey, I'd be happy to. Check your email box in a few minutes.

Tom

Ok... here's a copy of the document...

http://www.nonimitation.net/Nonrelativity.doc

Hi guys,

I've been really busy lately, but I am going to try to get documents written up for sections 2 and 3 of Ch. 1 (Fermions and Lie Algebra).

Physicsforums is back up, but their server is only letting them stay up until Monday. They are trying to move to a new server, but that might not happen by that time.

Here is the link to my thread at PF. Some helpful comments have been posted by some good people:

http://www.physicsforums.com/topic.asp?ARCHIVE=&TOPIC_ID=5584

Tom

Tom, you have written:


in my QM courses, I learned that the correspondence principle was simply i/hbar[A,B]_QM --> {a,b}_classical


the correspondence principle that you learned in QM does not always work like this.


a reminder:
the correspondence principle says turn your classical poison bracket into your quantum commutator. and then write your classical function with the classical canonical variables replaced by the corresponding quantum operators.

for example, if the classical function is qp, the quantum operator cannot be QP, but rather must be 1/2(QP+PQ). for functions of degree 3 or higher it gets more complicated. you have to also include some quantum anomoly terms, when taking the poison pracket to the commutator.

for example, one can show that the correspondence principle takes {pq²,p²q} = 3p²q² --> i\hbar/3[P³,Q³] + \hbar^2

that term on the end there means that we have to add a quantum anomoly term when we quantize the system, in order to be consistent with the assumptions of correspondence principle. but notice that the anomoly term is of order hbar^2.

you can also get quantum anomoly terms in your hamiltonian, when you, for example, try to quantize a noncartesian system. here again, the anomoly term is of order hbar^2.

so in the classical limit, hbar --> 0, and all variables commute.

in the semiclassical limit, divide by hbar, then take hbar --> 0, and the anomoly terms disappear, and the commutators simply become the poisson brackets, the hamiltonian becomes the classical hamiltonian.

i believe that there is no axiomatic way that is self consistent to specify the rules for quantization.

<hr>

tom, i haven t looked at any of those documents you listed as references, do they treat this issue?

is it clear what s going on here? i m getting this mostly from ticciati. also shankar has a bit about this.

i think this is what s going on with siegel, but i ain t positive, so i would appreciate any feedback.

let me explain that in a little more detail:

let s say that i have a classical system that i want to quantize. this means that i want to write down a mapping z that, at the very least satisfies the following conditions:

z(p) = P
z(q) = Q

z({f(p,q),g(p,q)}) = i*hbar [z(f(p,q)),z(g(p,q))]

where f and g are any functions.

naively, you might want the mapping to be a little stronger. you might want it to take

z({f(p,q),g(p,q)}) = i*hbar [f(P,Q),g(P,Q)]

but we will see that even the weaker condition above is not possible. using just these three assumptions, you can discover by considering all the commutators that z(p²)=P² + k, for some constant number k, and similarly for Q. then taking the poisson bracket of those two functions immediately shows that

z(pq)=1/2(PQ+QP)

so my second stronger condition above is violated. if i wanted to preserve the functional form of the observable, i would have to require z(pq) = PQ.

this fact is not so distressing however, because the classical variables commute, there is some ordering ambiguity. and furthermore, this symmetric sum is required to make the quantum observable hermitian.

however, the problem gets worse when you go to third degree functions.

you can calculate the poisson bracket for those third degree terms i mentioned above, and then plug in the mapping for that poisson bracket, and compare it with the commutator, you will see that the mapping no longer preserves the bracket to commutator isomorphism, except in the hbar --> 0 limit.

according to ticciati though, this is only of academic interest, since in QFT we never have to quantize systems with cross terms like that.

lethe,

That does help. I have yet to really dig into those documents I referred to in my notes, but they are a lot more complicated than your post. I will have a look at Ticciati if my school library has it. I took QM from Sakurai's book, and none of this was discussed. Are there any other books that talk about this correspondence?

Tom

Guys,

I don't have the energy to do this thread at two different forums. Since there are so many more physicists and mathematicians at PF, I'm sticking with that. Feel free to join me:

http://www.physicsforums.com/showthread.php?s=&threadid=23


Tom

Currently I am using LeBellac; if it is going to be a self-reading then it is better than Peskin-Sch. Note also that the people at superstringtheory.com are running a lecture group for the Peskin just now.

i believe that their is no axiomatic way that is self consistent to specify the rules for quantization.


Afaik, the trick is to specify a consistent rule of symmetrization of p and x along all the quantization process.