# Self-taught Quantum Field Theory

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 Is Mandl too outdated?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"?

Jon

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

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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
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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.

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.

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Jon2005 said:
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.
Well if you got even a little scattering and Klein-Gordon you might well be ready for QFT; the books normally start about there.

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 [Broken]

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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.

Jon2005 said:
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.
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.

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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.))

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.))

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

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

hi. i am also learning path integral and introduction to field theory, but somehow i don't like the lectures. i don't read books but only lecture notes. it covers path integral for boson and fermions, dirac field. i think i will fail this module.... if you guys can learn these stuff just from whatever books, please tell me.

argonurbawono said:
hi. i am also learning path integral and introduction to field theory, but somehow i don't like the lectures. i don't read books but only lecture notes. it covers path integral for boson and fermions, dirac field. i think i will fail this module.... if you guys can learn these stuff just from whatever books, please tell me.
I recommend two books:

1) L.H. Ryder Quantum Field Theory
2) P. Ramond Field Theory: A Modern Primer

These two books formulate the QFT using Path integrals
And these two books is not difficult to understand/

aav
I'm taking up QFT also. Here's my 2 cents:

I find the following books to be useful at my level (introductory)
(1) Greiner, Field Quantization: shows you in vivid, explicit detail the requisite calculations. I try to do them first on my own, of course
(2) Ryder, Quantum Field Theory: it's a nice "second" book. Insightful. The chapter on canonical quantization is a must read.

Also, in my case, I found it useful to do a bit of relativistic QM as preparation for QFT. Someone suggested Sakuarai's "Advanced QM". The chapter on the Dirac equation is excellent (never mind the ict).

CarlB
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argonurbawono said:
hi. i am also learning path integral and introduction to field theory, but somehow i don't like the lectures. i don't read books but only lecture notes.
There are two problems in learning QFT. The first is understanding the mathematics. If this is the problem, then you need to get as many books as possible. One of them will explain it in a way that you appreciate. In general, there are two difficulties, the Fourier transforms and conversion, and the group theory.

The second problem is understanding the physics. I think that this is best understood without the confusion created by the mathematics. If this is the problem, then you will know because you will have trouble explaining what the path integrals represent. Try this book by Feynman which is an introduction to QED for the general public:

https://www.amazon.com/exec/obidos/tg/detail/-/0691024170?v=glance&tag=pfamazon01-20

Carl

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I have the 1st edition of Ryder. Is it worthwhile upgrading to the 2nd edition?

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One of the things that bugged me about Ryder (I've had it and used it for years) was no excercises. Filling in "easy to sees" is not the same. I see that Ramond (which I only got in the past year, because of recommendation here) has problem sets and at they are specifically stated to be in order of increasing difficulty.

for example here is the first and last problem of the first set (covering elementary consideration of action functionals, which Ramond abbreviates AF). He directs: "...use the Action Functional as the main tool, although you may be familiar with more elementary methods of solution."

A. i) Prove that the linear momentum is conserved during the motion described by $$S = \int dt \frac{1}{2} m\dot{x}^2, \dot{x} = \frac{dx}{dt}$$
ii) If $$V(x_i) = v(1-cos \frac{r}{a})$$. find the rate of change of the linear momentum.

...

D.Given an AF invariant under uniform time translations, derive the expression for the associated conserved quantity. Use as an example a point particle moving in a time-independent potential. What happens if the potential is time-dependent?

Hey, glad to see other people regard QFT as worth learning in their spare time. You've got a fair start on me though as i'm trying to learn the math as I go. PDF Ebooks are great but you might be like me and enjoy reading away from your PC. If so I can recomend the following.

The quantum theory of fields- By Steven Weinberg (ISBN 0521550017)
Get volume one as it is more relevent to the theory instead of the practical applications in volume two. It's publisher is Cambridge University Press.

If you realy don't mind a purely math based interpretation try 'Quantum field theory of point particals and strings' by Brian Hatfield, Addison Wesley publishers. ISBN 020111982X (I couldn't get through this due to my math being poor but it has only a small amount of string theory towards the end.The book starts at first and second quantisation).

For an overview of the theory I'd suggest 'The undivided universe' by D Bohm and BJ Hiley, ISBN 0415065887. Publishers Routledge. For a truely philosophical blah session try 'An interpretive introduction to quantum field theory' by Paul Teller. ISBN 069101627.

This forum is a great idea. I live in Australia and find it realy difficult to speak to anyone outside University that enjoys physics or hard science. What i'd give to visit America or Europe.

vanesch
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I'll add my 2 cents too.
As some said, it is necessary to master "ordinary" QM before jumping into QFT, but then there are many aspects of ordinary QM which won't help you much for QFT.

My favorite "ordinary QM book" is "Modern Quantum Mechanics" by JJ Sakurai (not his "advanced QM" book which is much more known!).
It is not too thick, provides a lot of insight, it is not too hard to follow if you already had a first exposure, and in fact, it prepares well for QFT (in fact, that is what Sakurai had in mind with this book: teach quantum mechanics so that it prepares you for QFT).

I would also join others in warning you not to expect as clean an exposition of QFT as you have seen on many other physics subjects. In fact, QFT is troubled with a lot of shaky constructions, and a lot of effort goes to purely calculational tricks of the trade, funny ways to try to approximate solutions (which are not mathematically very clean) and so on.
So you should put your critical mind a bit more aside than usual, and just try to get the hang of it, by "imitation".

Personally, the book that got me started in QFT was Peskin and Schroeder. I know it has a lot of critique, often justified, but the first part is, I think, ok. It starts out with the canonical approach (which is not the modern way of doing things, but which comes closest to what you know when you learned quantum theory), and then explains you in painstaking detail, how to do all the calculations, with all the tricks. When you worked your way through the first part, you "master" the calculation of QED Feynman diagrams beyond leading order. That gives some kind of satisfaction: that you are really able to do those calculations (even though the procedures sound more like voodoo hocus pokus than any rigorous and understandable mathematical approach).

Zee is a totally different and complementary text: it tries to explain you, really in a nutshell, the main ideas involved. It lacks the technical details to allow you to do all the things yourself, but you get the bigger picture.

Nevertheless, I think that using Peskin to "get your hands dirty" is what gives you the necessary motivation to go on (now that you will be able to do some stuff really by yourself from scratch).

Weinberg is great, but not for starters. It's just too hard.