Self-taught Quantum Field Theory

Jon2005

I'm interested in teaching myself QFT. My BSc is in Mathematics and Physics, so I probably have a stronger mathematical background than the average physics graduate.
However, I'm assuming it's almost certainly not good enough.

What I am looking for is a way of sensibly teaching myself the topic, most likely beginning with the relevant mathematics.
As for the self-teaching part, it obviously won't be easy, but I'm doing it as a hobby, so I guess I can take as much time as I like. I also taught myself most of my university course anyway, so I have some experience with it.

Any ideas for the relevant background?

Beyond the mathematics obviously I want to get into the subject itself. What books would you recommend? Is Mandl too outdated? Zee too "flimsy"?

Thanks for your time
Jon

actionintegral

You said Quantum Field Theory. Do you know Elementary Quantum Mechanics?

selfAdjoint

You should know basic quantum mechanics, including being able to solve simple excercises, as actionintegral said. I think it would be a good idea to spec up also on advanced integration techniques, including distributions and functionals. QFT strongly depends on these techniques and IMHO they are not well-presented in any text; the normal way graduate physics students pick them up seems to be by word of mouth and example.

ZapperZ

As everyone here has mentioned, if you do not have any knowledge of advanced QM, no amount of mathematics can help you. This is especially true if you haven't mastered Second Quantization, because that technique (and its notation) will be prevalent all over QFT.

Zz.

Jon2005

Good points, I should walk before I run.

I did a few modules on QM at undergrad level, how do I know if they went far enough?
Off the top of my head, it went through the two formulations of QM, uncertainty principles, the hydrogenic atom, various particles in potentials, spin and angular momentum, measurement and philosophical blah, Dirac notation, variational method, perturbation theory (time indep and time dep) up to 2nd order, creation/annihilation operators, some scattering, klein gordon.

selfAdjoint

Well if you got even a little scattering and Klein-Gordon you might well be ready for QFT; the books normally start about there.

Dimitri Terryn

Not a bad idea at all. I can recommend this text

http://www3.imperial.ac.uk/portal/pl.../1/4865913.PDF

Astronuc

This text might also be useful -

A Modern Introduction to Quantum Field Theory (Oxford Master Series in Physics)
From the site provided by George Jones -
Table of Contents and Chapter 1 (pdf) - http://www.oup.co.uk/pdf/0-19-852073-5.pdf

Daverz

Learning some QFT is also on my TODO list, as I didn't make it there before dropping out of graduate school. I've ordered the book above, which looks good from the TOC, and also have Ryder (1st ed), an old, ugly copy of Ramond, the QED book in the Russian "Course of Theoretical Physics" series, and Weinberg's "Foundations" book (somewhat tedious).

There's also this online book

http://insti.physics.sunysb.edu/~siegel/errata.html

Which is linked all over the place. But I have to admit that I don't find the author's style very readable. But the material is certainly interesting.

I also found this draft of a book while googling:

http://www.physics.ucsb.edu/~mark/MS-QFT-11Feb06.pdf

Daverz

Here's a better link for that online QFT book: http://www.physics.ucsb.edu/~mark/qft.html

It looks pretty good so far.

He says it will be published by Cambridge, which is good because their books usually have semi-reasonable prices.

Perturbation

Some familiarity with relativistic quantum mechanics and Lagrangian/Hamiltonian mechanics/field theory would help, though they are skimmed over in most QFT texts. I've not read it, but Weinberg's "Foundations" volume looks like a fairly concise introductory QFT book that includes a fair amount of relativistic QM, I think I might get it in a couple of months. I used Schroeder and Peskin to teach myself QFT, or rather am still using it, but to be honest the first couple of chapters are some what lacking, they could do with being beefed up with some more field theory and relativistic QM (pretty much any mention of the Lorentz group and its algebra is left as an exercise and Poincare isn't even mentioned!), as they are very important to the rest of the book.

Chaos' lil bro Order

Read Feynman's book on QED for starters.

fliptomato

I jumped head first (perhaps a little too hastily) into QFT after a year-long QM course. Here are my thoughts on where to start:

1) Don't spend too much time reviewing quantum mechanics. You should be solid on creation/annihilation operators, as well as a few 'advanced topics' (Heisenberg formalism, Born approximation) ... but learning these things *really* well won't help as much as actually diving into QFT.

2) It sounds tautological, but QFT is a lot easier if you already know the 'punchline.' I found it very helpful to go through particle physics texts (especially Griffitihs Elementary Particles text) since they provide the nuts and bolts of how to calculate Feynman diagrams as well as the big picture of what you're trying to do with QFT (unless you're doing condensed matter). Your goal from these texts should be a working knowledge of calculating cross sections. Don't worry if things aren't terribly well motivated, you'll get to that.

3.) What overwhelmed me was that the subject was very rich in new ways of thinking that I couldn't differentiate between the 'big' ideas and calculational details--if you know what the big ideas are ahead of time, then digesting information from a "heavyweight" textbook like Peskin will be easier. For this reason, you might want to start with the Oxford QFT book ("An Modern Introduciton to QFT") which eschews most of the calculational details in favor of a broad picture.

4.) When you decide to really put your nose to the grind stone, you'll immediately have a choice. There are two formulations of QFT: the Path Integral formulation and Canonical Quantization. The "standard" QFT textbook, Peskin's "An Introduction to QFT," starts with Canonical quantization and doesn't use the Path Integral formalism until much later. Zee's "Quantum Field Theory in a Nutshell," which is more conceptual and friendly for beginners, focuses on the Path Integral formulation. You'll have to make a choice here, since I found that trying to refer back and forth between Peskin and Zee was difficult in the first few chapters becuase they were speaking different languages for the same physics.

5.) If you decide to start from Peskin, my favorite companion text is Griener's Field Quantization. It has several worked examples and spells out more of the nitty gritty for you. Zee is pretty readable compared to the other text. The first few chapters is all you need to get a solid flavor for what's going on. ((Actually, depending on your goals, Zee might be a perfectly good text by itself. If you want to calculate cross sections to 2-loop order, then you'll eventually want to read Peskin.))

fliptomato

Oh, by the way... Zee once said that "The only person who can read Weinberg is Weinberg." If you have a slightly weaker background than most students of theoretical particle physics (as I did when I took QFT), then I wouldn't suggest spending too much time reading Weinberg and instead start out with Zee/that pink oxford book. ((That being said, I hear the text is brilliant for those who follow it.))

joelperr

There's also the book "Advanced Quantum Mechanics" by J.J. Sakurai, which is considered a classic text in QFT.

Epicurus

QFT. You either get it or you don't, its one of those physics things that many don't get.

1-Don't use one book. Get as many point of views as possible,

2-QFT has many holes. Don't expect a self consistent theory here,

3-If you have a desire to learn this method it will sink in over time, just keep reading and working.

4-Calculate the corrections to the magnetic moment of the electron. If you do this and understand this, you shoud be able to formulate and evaluate your own ideas