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Possible Duplicate:
Best books for mathematical background?

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.

Community
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3 Answers3

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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.

For example,

  • Supersymmetry Algebras That Include Topological Charges
  • Search for a Realistic Kaluza-Klein Theory
  • A Simple Proof of the Positive Energy Theorem
  • Constraints on Supersymmetry Breaking
  • Dynamical Breaking of Supersymmetry
  • Global Aspects of Current Algebra
  • Current Algebra, Baryons, and Quark Confinement
  • Non-Abelian Bosonization in 2d
  • Strings on Orbifolds
  • Supersymmetry & Morse Theory
  • Baryons in the 1/N expansion
  • Verlinde Algebra & the Cohomology of the Grassmannian
  • Gravitational Anomalies
  • ...
user1504
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3

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.

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

Vijay Murthy
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