I am currently a Master's student in Mathematics. The main focus of my undergraduate programme was on Mathematics. However as a part of the course, I have done some Theoretical Physics courses. In mathematics, my area of interest is Topology-Geometry and I also like analysis. I have heard recently lots of exciting research is going on at the intersection of Top-Geo and QFT/String Theory (for example Witten's work/ Yang-Mills theory) and Mathematical Foundations of QFT etc. I am very eager to learn them/do my doctoral work in this direction (in some mathematics department). I shall highly appreciate any comment/guidance/advice in this direction. For example

  1. Can you please tell me name of some good books/lecture notes/lecture videos from where I can learn QFT, GR, Gauge Theory, String theory from a physicist's view point so that I get enough motivation/intuition to read books where they have been discussed with a greater mathematical sophistication? (I have downloaded quite a lot of books written in this direction including Quantum fields and Strings- A course for mathematicians, but unfortunately I cannot read any of them.)

  2. Can you tell me name of some mathematics department with an active Mathematical Physics research group?

  3. Any other advice regarding how should I proceed.

Sorry for such a long post and Thank you in advance

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    $\begingroup$ Better avoid string theory, it is pretty clear nowadays that it's a nice attempt from late 70s/early 80s, but failed to describe anything in physics. It was told me by my Professor working in string theory that people in the community are kind of depressed - that was a fews years ago, and things got worse. Even several of its developers (such as David Gross - see here ) are stopping one by one. $\endgroup$ – NicoDean Oct 6 '14 at 17:56
  • $\begingroup$ This might be way below your level, but here are some stanford video lectures by renowned physicist Leonard Susskind: theoreticalminimum.com $\endgroup$ – Winston Oct 12 '14 at 20:47

I am also a mathematics student who likes physics. My advice would be:

  • I learned a bit of QFT following Srednicki's book and Tong's lecture notes. A note: the book focuses mainly on the path integral approach, with very little in the way of S-matrix techniques.
  • For GR, I found Jetzer's lecture notes and, knowing the guy, Graf's lecture notes ought to be great.
  • I have learned String theory on some book, but I don't remember the title right now. If you want can look it up.

I think here at ETH there's a pretty good group doing mathematical physics, if you want to try to apply and to move to Switzerland.

Also general advice: If you are interested in a topic in physics, always look if Tong has written something on it. His lecture notes are usually very good.

  • $\begingroup$ Can you tell me the name of String theory books? $\endgroup$ – Bingo Oct 4 '14 at 16:01
  • $\begingroup$ @alphad When I get back to my apartment tomorrow evening I'll tell you. $\endgroup$ – Daniel Robert-Nicoud Oct 4 '14 at 16:22
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    $\begingroup$ @alphad The book of string theory is Basic concepts of string theory by Blumenhagen, Lüst and Theisen. $\endgroup$ – Daniel Robert-Nicoud Oct 5 '14 at 20:30

Felsager: Geometry, Particles and Fields might be a good starting point, since this author has some good pedagogy to offer.

ETH Zürich is indeed an excellent place. Other options could be Bonn, Faculty of Mathematics, HSE, Moscow, MIT, Columbia University, U Kyoto ...


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