I want to read about Wittens work, on Cherns-Simons theory, and relations to knots and jones polynomials. I am extremely motivated to read his paper: Quantum Field Theory and Jones polynomial.

What are the prerequisites in topology, geometry and QFT needed to understand this paper? I have good grasp of basic point-set topology concepts, and have read about manifolds(Nakahara). In QFT, I have just started QED. What do I need to study from each of these? As per my knowledge, I need some knot theory and cohomology(?), and quantum yang-mills theory. Is this correct? Also please provide references.

  • $\begingroup$ I can't claim to have understood even most of this paper, but one thing that isn't mentioned on your list is a bit of fibre bundle theory as applied to quantum gauge theories. Quite a lot of the paper is formulated in this language. Nakahara (chapters 9 & 10 at least) will be useful. $\endgroup$ – Mark Mitchison Jan 7 '13 at 16:29
  • $\begingroup$ Possible duplicate: physics.stackexchange.com/q/41589/2451 $\endgroup$ – Qmechanic Jan 7 '13 at 21:46

Yes this is the classic paper. You could start with QFT as in Itzykson and Zuber, Algebraic Topology in Bott and Tu and any of many good books on knots. Nakahara is also good. But bear in mind that the field has exploded since then and there are newer references that are easy to read, some with alternative viewpoints. The subject is known as TFT (see references at bottom of page). There's also Kassel on Quantum Groups, which is indirectly related through the category theory that underlies TFTs.

In summary the main prerequisite subjects are: QFT, TFT, algebraic topology, knots.


I recommend reading this first:

P. Cotta-Ramusino, E. Guadagnini, M. Martellini, and M. Mintchev. Quantum Field Theory and Link Invariants. Nuclear Physics B, B330:557, 1990.

Also Guadagnini has a nice book("The Link Invariants of the Chern-Simons Field Theory") on the subject but it is hard to find.


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