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 Is Mandl too outdated?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]

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.

 

[Kalimaa23]

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

http://www3.imperial.ac.uk/portal/pls/portallive/docs/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]

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.

 

[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

 

[argonurbawono]

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.

 

[PRB147]

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]

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:



Carl

 

[Daverz]

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

 

[selfAdjoint]

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?

 

[David Burke]

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 recommend the following.

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

If you really don't mind a purely math based interpretation try 'Quantum field theory of point particles 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 truly 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 really difficult to speak to anyone outside University that enjoys physics or hard science. What i'd give to visit America or Europe.

 

[vanesch]

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.

 

[selfAdjoint]

Patrick, I have to disagree about Peskin and Schroeder; I believe it is unsatisfactor at the start ("trust me" over and over again, which promise is not really fulfilled, and really lame motivations of things), and gets a little better later. Of course it does get you up to speed on Feynman diagrams and two-point functions real fast, and that's what a lot of students want.

 

[vanesch]

Patrick, I have to disagree about Peskin and Schroeder; I believe it is unsatisfactor at the start ("trust me" over and over again, which promise is not really fulfilled, and really lame motivations of things), and gets a little better later. Of course it does get you up to speed on Feynman diagrams and two-point functions real fast, and that's what a lot of students want.

That's what I tried to say, too. Don't read Peskin for any deep conceptual understanding, but it *is* rather good at getting you up and running at doing actual calculations with all the tricks. I don't know of any other book which teaches you so easily to actually *calculate* things. It's a kind of a Schaum's Series "how do I calculate feynman diagrams" (I exaggerate a bit here...)

 

[antoniobernal]

Hi, this is my first post in this forum, glad to see there are people close to my current situation,

I've been trying to self teach me QFT for some time and I always found that the concepts introduced by the books where disconnected with my previous knowledge on QM. (I suppose this can be a signal of poor understanding of QM on my part.)

Anyway, there is a review in Amazon on the book by Mandl Quantum Field Theory,

https://www.amazon.com/gp/product/0471941867/?tag=pfamazon01-20

that makes a strong point that precisely that book should be the only first book to be taken by a beginner. Despite its age, the review goes, this book takes your hand and shows you the basic stuff step by step.

I don't know what your feelings regarding Mandl are, I have looked slightly at it and it seems to start low enough to catch with an ordinary knowledge of QM.

There is also the book by Lahiri&Pal,

https://www.amazon.com/dp/0849309778/?tag=pfamazon01-20

that some people say is better than Mandl. Reading the TOC, they both look like similar "level-zero" introductions to QFT, but if someone has gone through them, perhaps he could give a more informed opinion.

One drawback of those two books is that they don't even touch path integrals, so after them one should continue with more advanced/modern texts, perhaps Brown, Zee or Srednicki.

Any ideas/suggestions?

Thank you

 

[CarlB]

I've been trying to self teach me QFT for some time and I always found that the concepts introduced by the books where disconnected with my previous knowledge on QM. (I suppose this can be a signal of poor understanding of QM on my part.)

Before you suffer through learning QFT the way all the rest of us did, you might try taking a quick look at the excellent arXiv article that just recently came out:

Quantum Electrodynamics of qubits
Iwo Bialynicki-Birula, Tomasz Sowinski, May 15, 2007
Systematic description of a spin 1/2 system endowed with magnetic moment or any other two-level system (qubit) interacting with the quantized electromagnetic field is developed. This description exploits a close analogy between a two-level system and the Dirac electron that comes to light when the two-level system is described within the formalism of second quantization in terms of fermionic creation and annihilation operators. The analogy enables one to introduce all the powerful tools of relativistic QED (albeit in a greatly simplified form). The Feynman diagrams and the propagators turn out to be very useful. In particular, the QED concept of the vacuum polarization finds its close counterpart in the photon scattering off a two level-system leading via the linear response theory to the general formulas for the atomic polarizability and the dynamic single spin susceptibility. To illustrate the usefulness of these methods, we calculate the polarizability and susceptibility up to the fourth order of perturbation theory. These {\em ab initio} calculations resolve some ambiguities concerning the sign prescription and the optical damping that arise in the phenomenological treatment. We also show that the methods used to study two-level systems (qubits) can be extended to many-level systems (qudits). As an example, we describe the interaction with the quantized electromagnetic field of an atom with four relevant states: one S state and three degenerate P states.
http://www.arxiv.org/abs/0705.2121

Basically, the idea above is to strip QFT down to its essentials. Eliminate all position dependence (which creates all those nasty integrals and is responsible for all that nasty Poincare symmetry), and look at the use of QFT on the qubit system, that is, on the simplest possible quantum states.

I am writing up a post on the subject on my blog and will put it up here probably within 24 hours:
http://carlbrannen.wordpress.com/

My post will be even simpler than the above article.

 

[Haelfix]

People have already spelled out the good QFT recommendations. But its hard to just jump into the subject without a second advanced QM course, which people don't always have as an undergrad.

I recommend students in general to start with a good intro primer on particle physics before jumping into the full fledged theory perse. First get a handle on the lingo, some of the particle zoo phenomenology and to get some intuition about group theory and a cursory review of the Dirac/KG equation, scattering theory and then eventually calculating Feynman diagrams.

The perfect text for an undergraduate then is Griffiths, Introduction to Elementary particles. The theory books then that follow (eg Zee, P&S, etc etc) basically derive and justify the methodology that's used.

I know many experamentalists who basically have forgotten most of the nitty gritty details of the full theory perse, and instead work with the sort of level of rigor that Griffiths uses.

 

[captain]

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.

what is "Second Quantization"?

 

[captain]

I was also wondering if "Quantum Theory" by David Bohm is a good book advanced quantum mechanics?

 

[Nigel Hall]

Self-taught Quantum Theory

Sakurai's Modern QM has a chapter on Path Integrals, which shouls make a good jumping-off point.

I am looking for anyone who has successfully completed the "excercises" in Ramond. Some of them seem very difficult. So much so that I can't always relate them to the material covered in the chapter!

 

[exponent137]

One of the best books of QFT is written by Eugene Stefanovich. Its book is on arxiv.

But how I wish to understand QFT:
"imagination of all formulae. All formulae write differently, so that we can see their aspects. All mathematics is imaginable. Example is Brukner's thesis. It can also be found on internet." OK, Nikolic in its Myths... also wrote similar analysis of spin matrices as Brukner.

One of the largest reserve for the theory of everything is to write clear theory of QFT. After this you will find many peoples, which will find TOE.
Not "milion" of researchers in strings but "milion" of writers of clear QFT.

We live in computer age, where only lack of imagination is obstacle to clearer QFT. Here it is a lot of experts of QFT. If every one analyses only one formula of QFT as Brukner did for QM, the new book will be here.

 

[shadowpuppet]

For those who enjoy a 'classroom' setting, here are
Sidney Coleman's Lecture Notes on RQM and QFT:

Notes:

http://www.damtp.cam.ac.uk/user/dt281/qft/col1.pdf

http://www.damtp.cam.ac.uk/user/dt281/qft/col2.pdf

Lectures:

http://www.physics.harvard.edu/about/Phys253.html

Try this book by Feynman which is an introduction to QED for the general public:



Carl

I really love that book, it makes clear what the challenges of QFT are for the
general public and even shows the frontiers of the field as seen by Feynman.

 

[reilly]

Jon2005 -- As a physics professor, I developed a common sense approach to mastering most any subject, including QFT, which I outline below. From freshman to graduate students, those that followed these steps were consistently my best students; they all got As and really knew their stuff.

At the beginning the approach will be difficult and time consuming -- it might take several days just to get through a couple of pages. But as you continue, the process will become much easier, and will be increasingly fruitful. Among other things, this approach provides a very efficient way to build your intuition. The process really works. So, here are the steps

1.Get two or three QFT book; initially it makes little difference which ones.

2. Throw away all yellow -- or red or...- marker pens

3. Get a big notebook, a ream or two of plain paper, and many of your favorite writing instruments.

4. Pick one of your books, and read Chapter 1.

5. As you read , write out everything you think important in your notebook, whether text or math. Do not write in or mark the book.

6. And do every computation in the Chapter; that's what the plain paper is for. The notebook is for discussion of the important computations -- by your measure.

7. If you get stuck, keep going -- you can almost always trust your text -- and write in your notebook, where and why you are stuck.

8. At the end of this process, you have your own summary notes of Chapter 1, and a list of "stucks". Review them, refine them and then write them as an essay or paper. You might also find, that you need to backtrack to bring your physics-math background up to speed.

9. Go to the other books and check whether or not they can help you with your "stucks", and check whether they might be better candidates for your study.

10. Do the homework problems ; makes sense to use a text that provides answers to these problems.

11 Go to Chapter 2, and repeat the process.

12. At the end, you will have clean textbooks, and your own QFT text, including discussions of stuff you don't get. Through the acts of writing the important things down, and constantly refining your notes, you will develop considerable mastery of QFT as presented in the books you use.

13. Beg, borrow or steal assistance -- books, the Internet, this Forum, individuals -- to help you with things you don't get. In many instances, you'll find your further study will nicely illuminate tough issues.

Good luck, and regards,
Reilly Atkinson