First post - I've been thinking for a couple weeks about how to present this. About 20 years ago I was a grad student in physics and fizzled - did lots of coursework but never got a Ph.D, and have been working as an electrical engineer since. (Note to other's who are thinking of dropping out - don't do it, you'll regret it forever.) For the past year or so I've been reading physics again and have become very interested in quantum field theory. My study was never in this area and I find myself with a huge hole with respect to the math. I just started working through Stephen Weinberg's "Quantum Theory of Fields" but don't have the foundation for even the "foundations" text. In parallel, I've been reading "Rotations, Quaternions, and Double Groups" by Simon Altman which fills in some gaps but really not enough. I'm soliciting advice here about how to fill in the gaps with your suggestions regarding reading material or other alternatives. I'm not opposed to attending lectures but I'm thinking that this material isn't so new that there should be lots of different ways to self-educate. thank you - Mark Sheffield
Hi Mark, Welcome to Physics Forums. Are you primarily interested in relativistic field theory? If so, I would recommend the following three books for self study: 1. Quantum Field Theory in a Nutshell by Zee 2. Quantum Field Theory by Srednicki 3. A Modern Introduction to Quantum Field Thoery by Maggiore 1. is a conceptual favorite for many people, and it gives a flavor of the subject without getting bogged down in details. This book is good for getting a fresh perspective after doing a long Feynman diagram calculation. 3. is nice little book with lots of problems which will supplement your calculational ability (although among qft books its not regarded as particularly calculationally intensive), something hard to get from Zee. It's also conceptually nice as well. 2. is a longer more systematic book which is nevertheless quite modular. This enables you to study those topics you feel weakest on while seeing how they explicitly relate (in Srednicki's opinion) to everything else. All these books are thoroughly modern and up-to-date. Weinberg remains a very nice general reference to which you will probably return more and more as you gain experience and intuition. I too began my study of qft with weinberg, but it's just really hard to get going when you try to be as general as weinberg. Hope this helps. PS It's a great idea to ask questions on PF as well. There are many smart and friendly people here who can help you out.
Thanks for the reply - I did a quick look at the Zee book on Amazon and I've never seen anything that blends prose with math this way. Well, maybe Feynman's lectures, but I certainly haven't seen it often. I also did a check on the contents and it hits the relevant areas - exactly the sort of thing I'm looking for. I won't be shy about asking questions on the forum - I expect I'll be doing this as I try to become more familiar with the material good advice & thank you - Mark
Hi Mark, I think it's a great idea to get back into it! I hope I can be of some help. First off, I think Weinberg's book is great for reference, but is certainly not meant to be introductory. To the above reference list I'd add a nice and rather light intro text -- Quantum Field Theory by Lewis Ryder. Good blend of conceptual and mathematical development. If you are interested in particle physics at all, Griffiths particle book is a stimulating introduction.
I am in the same situation as you, look at my profile. I have spent more than $6000 dollars on books. I have at least 15 books on QM, 10 on QFT. tens of books on all sort of mathematics, history of mathematics, philosophy of mathematic/physics,popular books on math/physics ...etc. Dover has a complete set of cheap books. Read arxiv. Did you know that P. Dirac was a EE major. you can go to a university library and sift through all the books. You can never get the picture from limited resources, you have to go through most of them, that is if you really want to get to the bottom of it.
bapowell and qsa - thank you as well I'll put these on the list (or bookmark this link, that's probably better). I agree that when all is said and done, I'll probably have a lot of books. I've gotten 6 or so over the past year, so I'm feeling a little bit like a book whore and will probably feel this way until I get some traction here. Particle physics is a further goal - what I'm trying to do here is get the first layer of the onion peeled back. What really started me off on all of this - the spark that hit the tinder - was Frank Wilczek's book "lightness of being" which prompted me to pull his paper on asymptote-free behavior (from the 70's) and some others. What hit home was that I really didn't understand the framework and math behind it all and I was stunned that I was so lost - after all, I was a Ph.D. student a few (more than a few) years ago. So I've been spinning my wheels in different ways with different books over the past year and a half and I think I finally have an image of where I'm trying to go. Further suggestions and ideas are welcome, please keep them coming thanks to all - Mark
From my experience the math for most purposes is not that bad, once you get the hang of it. But the confusion comes from the physics, which makes the math look so contorted. For one, there are three formalisms, the operator, the Schrödinger and the path integral and they jump between these pictures like a yoyo without any notice, so that is where you can get lost. Second, the system typically goes like lagrangian-->symmetry--->algebra --->geometry … so on, so the rational becomes confusing, especially when the steps are so long. Then the Hamiltonian pops out of nowhere and disappears just the same. Physicists are smart people, but don’t count on them for being good teachers. I have watched Susskind lectures and it will bore you to death. One problem, of course is that they have to keep the book on a manageable level. A Third problem with self-learning physics is that you will not have contact with experiment, so it is very hard to grasp some concepts. I guess you do not want to touch just yet the math of TQFT like category theory. And certainly you don’t want to go into non-commutative-geometry (QG); otherwise you will burn quite a junk of your neurons. These are just some of the problems. P.S. checkout “QFT of point particles and Strings” by Brian Hatfield, it is comprehensive and somewhat lucid.
David Tong has nice notes http://www.damtp.cam.ac.uk/user/tong/qft.html And so does Albert Stetz http://www.physics.orst.edu/~stetza/Book.pdf
Hi folks - I'm bumping this up for a further question (can I do this, or should I open a new topic?) I've been working on QFT in a Nutshell by A. Zee - am in the second chapter (chapter 1 was outstanding), and it's becoming more apparent that I need to do some work on bringing along my understanding of the math behind general relativity as I've never had a proper course in it - even in grad school. I thought that I could bluff my way through QFT without this, but now I'm thinking not. I'm looking for a book suggestion on par with the Zee book that derives/defines and explains the matrix/tensor math, the metrics, Minkowski spacetime. Is there a "Relativity in a Nutshell" out there? thanks - Mark
Hi Mark, Have you tried Weinberg's "Gravitation and Cosmology", or are you looking for something a bit more light weight?
Hi bapowell - thanks for your suggestion (as well as your previous ideas here) I think that I could get through the Weinberg book. I could only see the TOC on Amazon, but it didn't seem to be too esoteric (if you have a different opinion, please let me know). I have enough basic education in relativity from undergrad, but never needed to develop any skills with the math more than Lorentz-Fitzgerald contraction. It's pricey, isn't it? Maybe I can find it through a library to see if I can check it out prior to buying it. thanks again for your suggestion - Mark
As I recall, there's a pretty good introduction to special relativity and tensors in "a first course in general relativity". I don't think there are any really good introductions to SR, but I don't think you need one if you just want to understand Weinberg. If you make sure that you understand the stuff in these three posts, you will understand almost everything that Weinberg says about SR, matrices and tensors. https://www.physicsforums.com/showthread.php?p=2514428 https://www.physicsforums.com/showthread.php?p=2367047 https://www.physicsforums.com/showthread.php?p=2082559 You should probably get a good book on linear algebra. I like Sheldon Axler's "Linear algebra done right". If you want to read about representations of Lie groups and Algebras, I like Brian Hall's book (it focuses on matrix Lie groups, so you don't need to know differential geometry). If you'd like to refresh your memory about basic quantum mechanics, you should get Isham. If you want to go beyond that, Ballentine is the best advanced QM book. If you're going to study differential geometry, I like Lee's books "Introduction to smooth manifolds" and "Riemannian manifolds". The former contains a lot about tensors, and also Lie groups and algebras.
Thank you, Frederik. I've skirted through tensors in the past but never had to put them to use. I don't see a great mystery there, though, just a problem with severe rust and little fluency. The real issue is that a great deal of language (developed along with the math or because of the math) has developed in relativity that applies to qft. In what I've worked through, I'm using the symbols without understanding what they really mean so I find that I am off in the weeds quite often. I have so many gaps to fill in and it's not that I've forgotten the material (although I struggle to remember lots of things), its that I've never covered the material in the first place. Maybe weinberg is a good way to be sidetracked for a while. It will take a little work to tell. rgds - Mark
Mark, Yeah, Weinberg is pricey, but you can probably find a cheap(er) international edition. It was a required text during grad gr, but some of the students avoided doling out the cash by reading Sean Carroll's lecture notes: http://arxiv.org/abs/gr-qc/9712019 I've looked through these in the past and remember them being quite pedagogical and clear.
The best book I know of is GRAVITATION by Misner, Thortone and Wheeler. It goes through the math and the physics.
Thanks to all - I have enough to go with here. I downloaded the Sean Carroll notes (while the Weinberg book is in transit) and they seem to be a really good starter course and very explanatory. Just what the Dr. ordered. This is a very helpful group of people regards to all - Mark