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I am interested in learning the Chern-Simons approach to the fractional quantum Hall effect right from the basics. I have learnt about Lie groups and Weyl quantisation and am currently learning quantum field theory.

Can you please suggest in what order and what topics I should study?

Any help is appreciated.

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In order to quantize Chern-Simons a la canonical quantization, you choose a two dimensional spatial slice and impose commutators. It turns out that the theory that lives on this 2d slice is a 2d Kac-Moody algebra, i.e., a Wess-Zumino-Witten model. Therefore, a very important prerequisite is to understand the dynamics of such 2d theory. Chapters 13-15 of Di Francesco et al.'s book on CFTs are very good. While you're at it, chapters 16 and 17 are useful too, but don't worry too much about the details.

Once you're comfortable with WZW models you should read Witten's original paper on the Jones polynomial. It is still the most readable presentation of Chern-Simons theories, by far. Read this paper as many times as you need. When you are comfortable with Di Francesco & Witten, you basically know all you need about CS theories. Godspeed.

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