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  Structured and streamlined path to advanced theoretical physics for a mathematician with no physics background.

+ 2 like - 0 dislike

I'm a pure mathematician working in Ricci flow, Einstein manifolds, and Yang-Mills, with no physics background.  I'd like to learn advanced theoretical physics such as quantum field theory, string theory, and supersymmetry.  However, the standard books in these areas have very strong physics assumptions on the background of the reader, so they are inaccessible for a pure mathematician with no physics background.

Furthermore, after getting some way through mathematics, one realises that working through the big thick 1,500 page calculus textbooks is unnecessary since they are targeted at engineers.  Instead, one can start with books on set theory, logic and proof, and then go straight to pure mathematics books in analysis, abstract algebra, topology and geometry, etc.  I wonder if it's the same situation with theoretical physics: does one really need to start with working through one of those 1,500 page physics for scientists and engineers textbooks, or is there a better path?

Question:  As a pure mathematician with no physics background, how do I learn the basics through to advanced theoretical physics in a clear, focused, streamlined and structured way? 

Can someone please outline a path of study, with specific book recommendations, to achieve this?

asked Jul 3, 2015 in Resources and References by gds (0 points) [ revision history ]
edited Jul 3, 2015 by gds

1 Answer

+ 4 like - 0 dislike

With your background, the quantum field theory books by Zeidler are the ideal entry point. They assume a thorough knowledge of mathematics but essentially no physics, and introduce material up to research level, with lots of additional references for further reading. From the preface to Volume 1:

I have noticed that many of my colleagues in mathematics complain about the
fact that it is difficult to understand the thinking of physicists and to follow
the pragmatic, but frequently non-rigorous arguments used by physicists. On
the other hand, my colleagues in physics complain about the abstract level
of the modern mathematical literature and the lack of explicitly formulated
connections to physics. This has motivated me to write the present book and
the volumes to follow.

It is my intention to build a bridge between mathematicians and physicists.

He achieves this goal quite well. Three of the six volumes planned are already available. 

answered Jul 4, 2015 by Arnold Neumaier (15,787 points) [ revision history ]
edited Jul 6, 2015 by Arnold Neumaier

This is probably a stupid question but do volumes IV, V, and VI exist?  Are they still being written?

As far as I understand they are in the process of being written. Since the author's point of view is quite different from the usual one, it is a lot of work to compile such a volume. The later volumes are probably more difficult to write, which would explain the time lag.

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