# Tag Info

20

I am somewhat biased towards condensed matter physics, even though the subject extends also to fields such as cosmology and QCD. In the context of condensed matter physics I recommend the following books (even though various techniques also apply outside this regime): Rammer's Quantum Field Theory of Non-Equilibrium States. This was my first read on it, ...

18

Dear Eliza, matrix string theory may be viewed just as a variation of BFSS Matrix Theory, although arguably an important one, and the original papers are the full introductions at the same moment. http://arxiv.org/abs/hep-th/9701025 http://arxiv.org/abs/hep-th/9702187 http://arxiv.org/abs/hep-th/9703030 Some of the few hundred followups deal with ...

15

If you're a mathematician and you want to understand QFT, you're going to have to grapple with renormalization sooner or later. Your life will be easier if you understand from the beginning that the Wilson-Weinberg-etc 'effective field theory' philosophy is the essential organizing principle for the whole subject. In particular, you're going to need to ...

14

There are two aspects to this question: 1) Which sources try to communicate the usual vague and speculative physics story in a way that mathematicians are more likely to appreciate? 2) Which sources try to give an actual mathematical treatment of QFT, something that lives up to being maths? For the first, Deligne et al's Quantum Fields and Strings is ...

13

I have written a pedagogical article about renormalization and renormalization group and I would be happy to have your opinion about it. It is published in American Journal of Physics. You'll find it also on ArXiv: A hint of renormalization. B. Delamotte

12

1) The pioneer of the rigorous treatment of thermodynamics is Constantin Carathéodory. His aticle (Carathéodory, C., Untersuchung über die Grundlagen der Thermodynamik, Math. Annalen 67, 355-386) is cited everywhere in this context, but probably you want some newer and more modern things. 2) Buchdahl wrote a lot of papers about this subject in the 40's, ...

12

The Ising model is a model, originally developed to describe ferromagnetism, but subsequently extended to more problems. Basically, it is an interaction model for spins. Imagine you have a system which is a collection of $N$ spins. Each spin $S_i$ has two possible states $+1$ or $-1$. Here you can imagine already a possible extension to more states. You can ...

11

Renormalization is absolutely not just a technical trick, it's a key part of understanding effective field theory and why we can compute anything without knowing the final microscopic theory of all physics. One good online source that explains a nice physical example is Joe Polchinski's "Effective field theory and the Fermi surface" (and you can also look up ...

11

As it is, differential forms don't tell you the whole story--strictly speaking, differential forms only deals with covectors and wedge products of covectors and then uses the hammer of the Hodge star to be able to clumsily do inner products. To me, it is too far removed from the vector calculus you may already know. Instead, I strongly urge you to look ...

10

there is a book titled "Group theory and Physics" by Sternberg that covers the basics, including crystal groups, lie groups, representations. I think it's a good introduction to the topic. http://www.amazon.com/Group-Theory-Physics-S-Sternberg/dp/0521558859 to quote a review on Amazon (albeit the only one) "This book is an excellent introduction to the ...

10

Moshe has already addressed many points. You might be interested in Folland's Quantum Field Theory: a tourist guide for mathematicians. He tries to do as much things as possible in a mathematically rigorous fashion, and points out those points where this cannot be done. As for the mathematical background: some familiarity with partial differential equations ...

10

Kevin Costello, a mathematician, has written a book on quantum field theory, particularly the perturbative aspects. The book used to be available from his web page, but it has now been published by the AMS. You can find the links in his webpage to which I linked above.

10

I would really recommend the book by Frankel, The Geometry of Physics. He deals with all the fundamental concepts of topology and differential geometry, but gives clear and detailed applications to classical mechanics, electromagnetism, GR and QM. He is not too formal, but develops really a lot of useful tools using differential forms. Another book, which ...

9

You can perform $\LaTeX$ search - that is, write formula in LaTeX in an appropriate search engine: http://www.latexsearch.com/ However, as one can type the same expression in different ways and with different symbols, I never used it it practice. (Anyone did?)

9

Peskin and Schroeder tends to be the book used in most introductory QFT courses, so you'll definitely find all things there done in a pretty detailed way. Warren Siegel has an online book which is also pretty good, Fields.

9

JETP english archive (73-96), may be found here http://www.jetp.ac.ru/cgi-bin/e/index . Russian archive also starts at 73, so I think earlier versions may be found in libraries only. I found some issues of Proceedings of the RAS here: http://elibrary.ru/issues.asp?id=7781 in Russian only. It seems that they are not translated at all. And normal electronic ...

9

I agree with Ron Maimon that Large scale structure of space-time by Hawking and Ellis is actually fairly rigorous mathematically already. If you insist on somehow supplementing that: For the purely differential/pseudo-Riemannian geometric aspects, I recommend Semi-Riemannian geometry by B. O'Neill. For the analytic aspects, especially the initial value ...

9

Astrophysics is a big field. There are a variety of resources that you can use if you'd like to learn about how we know what we know. Most good textbooks will teach you this. In fact, I've even read a standard community-college level astronomy book (which contained basically no mathematics at all) that conceptually explained how we can infer certain things - ...

9

As a general rule, particularly in the sciences, the best people to ask for recommendations for books are second year graduate students in the field. You really get to know how well you learned something when you need to use it; for example, in a class for which it is a prerequisite, and you get to know which references are the best when you need them. In ...

9

Among normal books, Becker-Becker-Schwarz probably matches your summary most closely. However, you may want to look at a list of string theory books: http://motls.blogspot.com/2006/11/string-theory-textbooks.html Don't miss the "resource letter" linked at the bottom which is good for more specialized issues such as string field theory. An OK review of ...

8

I really like The Princeton Guide to Mathematics (Amazon, Google) Even though I believe it was meant more as a sort of Encyclopedia rather than an actual Textbook, I really like to read it as a "normal" book. Basically, whenever I understand some new mathematical concept I look it up in the Guide and see how it branches out and often find new interesting ...

8

:-) The best gentle introduction to basic twistor theory that I know of is the book by Huggett and Tod If you don't have access to that book and some other answers don't surface in the meantime I'm happy to write a few bits and pieces here, but will have to wait until the weekend. (I may be biased, but I think it's well worth learning, as the MHV ...

7

I would definitely recommend David Griffiths' book on particle physics. I don't have my copy with me right now, but as I recall, the book explains what the different particles of the Standard Model are, as well as the various properties of particles that are important in modern particle physics. It also introduces the basics of quantum field theory, just ...

7

There are a number of high level mathematicians who are working on giving a more mathematically precise description of perturbative QFT and the renormalization procedure. For example there is a recent paper by Borcherds http://arxiv.org/pdf/1008.0129, work of Connes and Kreimer on Hopf algebras and the work of Bloch and Kreimer on mixed Hodge structures and ...

7

Успехи физических наук 1918-2011 years For example - А.М. Прохоров, Н.Г. Басов Молекулярный генератор и усилитель УФН 57 (11) (1955) English version - Physics-Uspekhi 1958-2011 years

7

Skip to the last paragraph for the bottom line, otherwise read on: First you need to take more of the core math sequence to learn vector calculus, and at every chance you get you should try to deepen your intuition for it (what does it mean physically when you evaluate the divergence of a vector field, etc). Then you'll probably want to take classes (often ...

7

A perfect example for what I think you are looking for is J.S. Bell's Speakable and unspeakable in quantum mechanics (Amazon, Google). Although it is a collection of papers, this is a very readable account of some aspects of quantum foundations.

Only top voted, non community-wiki answers of a minimum length are eligible