I think the 'best' book in your scenario is " Geometry, Topology, and Physics " by Nakahara. I put this in quotes because I don't think it teaches the physicists true rigorous math (it just skims the surface with a bunch of terminology and only hands you the tools needed to compute some things in physics)... I've tried conversing with all my theoretical physics friends after they learn Algebraic…
For topics related to quantum mechanics, I recommend "Mathematical concepts of quantum mechanics" by Gustafson and Sigal. http://books.google.de/books/about/Mathematical_Concepts_of_Quantum_Mechani.html?id=SxzfDFfeQY8C&redir_esc=y
Arnold's "Mathematical Methods of Classical Mechanics"
Mackey's "Mathematical Foundations of Quantum Mechanics"
Barut's "Electrodynamics of Fields and Particles"
Stewart's "Advanced General Relativity" For quantum field theory/particle/standard model, read the original papers and a couple undergraduate textbooks. Remember that mathematical physics is still a branch of physics, so that if you thin…
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 …
"Equations of Mathematical Physics" by Vladimirov V.S. is great in terms of mathematical rigour. In fact, it emphasizes on maths, not physics, and that gives better understanding of further physical problems. You can find it here
