Mathematical Physics Book Recommendation

Question

I want to learn contemporary mathematical physics, so that, for example, I can read Witten's latest paper without checking other sources again and again to find some basic definitions and theorems. I know it need a long time and intensive efforts, but are there any good books related so that I can follow them in one or two years? I have learned physics theories that come before the quantum field theory, including general relativity. And I know differential geometry, category etc....

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Comments

Mathematical physics is just too broad at this point. If you pick a particular area, people can point you to useful references. As a start, you can't go wrong reading Nakahara's, "Geometry, Topology and Physics, and Nash's "Differential Topology and Quantum Field Theory". And learn quantum field theory.

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I don't think you can expect useful advice without narrowing things down, you'll just get everybody's favorite math book, which will send you on a wild goose chase. There are many math physics books because each one had different purpose, you'd have to decide what is yours.

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This question seems rather vague and not well suited to this stack exchange.

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Since you are relatively new, please take a look at [how to ask](http://theoreticalphysics.stackexchange.com/questions/how-to-ask) in the FAQ. As others point out, you should try to narrow your question; researches from different fields use different mathematical tools. For example, these book-request posts are more answerable: [one](http://theoreticalphysics.stackexchange.com/questions/794/readable-books-on-advanced-topics), [two](http://theoreticalphysics.stackexchange.com/questions/89/what-is-a-good-introduction-to-integrable-models-in-physics).

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And this [one](http://theoreticalphysics.stackexchange.com/questions/971/mathematical-rigorous-introduction-to-solid-state-physics) written by a student.

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Answer 1

Start by reading Witten's early papers. He wasn't able to expect his audience to know all the math already, so he often did a very nice job of explaining it.

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Answer 2

I have not read Witten's papers, but if you're willing to look at a senior undergrad, first year grad, text, I'd suggest Hassani's. It is very broad in scope, and provides a good introduction to a number of areas of mathematical physics.

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Answer 3

This is quite late. I found Mathematical Perspectives on Theoretical Physics: A Journey from Black Holes to Superstrings quite suitable for what you ask.

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Comments

The Table of Contents of this book does look very tempting. How did you perceive this book? The Amazon reviews seem to be very negative

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I do not work in String theory. So I do not wish to say anything about the review in Amazon. I use the book as a reference and handbook for the mathematics.

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