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From a physicists point of view, I would start with the following notes, which are Chapter 9 in John Preskill's Quantum Computing lecture notes: http://www.theory.caltech.edu/~preskill/ph219/topological.pdf, as well as the references within. I would also mention Kitaev's paper https://arxiv.org/abs/cond-mat/0506438 as a specially influential reference. ...


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I found this paper in Numdam's (a mathematical journal compilation) archive, which encompasses all that you talked about and I found it clear, with some references to Witten as well. This paper goes much further in detail, but I did not read all of it. And this might help if you aren't bothered by learning by forum posts?


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Topological terms of all types are always required not to depend on the metric, so their integrals will correspond to topological invariants, which serve as topological charges in quantum field theory. However, it is important to distinguish between two the types of topological terms mentioned in the question, because they lead to different physical ...


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I'm glad you asked! In the last decade, there have been incredibly exciting developments which have showed that the connection between QFT and knot theory is even deeper than previously expected. Let me first give a bit of a conceptual sketch, both of past and recent developments: In the 1980's, Witten realized that calculating Wilson loops in TQFTs in ...



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