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Mathematical Physics Book Recommendation

+ 6 like - 0 dislike

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....

This post has been migrated from (A51.SE)

asked Dec 15, 2011 in Resources and References by braill (0 points) [ revision history ]
recategorized Apr 24, 2014 by dimension10
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.

This post has been migrated from (A51.SE)
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.

This post has been migrated from (A51.SE)
This question seems rather vague and not well suited to this stack exchange.

This post has been migrated from (A51.SE)
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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3 Answers

+ 6 like - 0 dislike

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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answered Dec 15, 2011 by user388027 (415 points) [ no revision ]
+ 2 like - 0 dislike

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.

This post has been migrated from (A51.SE)
answered Dec 16, 2011 by rcollyer (240 points) [ no revision ]
+ 1 like - 0 dislike

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

This post has been migrated from (A51.SE)
answered Mar 4, 2012 by Vijay Murthy (80 points) [ no revision ]
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

This post has been migrated from (A51.SE)
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.

This post has been migrated from (A51.SE)

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