Deformation Quantization

Question

I am a beginner and I want to learn about deformation quantization. Please suggest me with which book or notes, I should start?

This post imported from StackExchange MathOverflow at 2017-09-17 21:04 (UTC), posted by SE-user satyendra

Comments

Do you have something specific you would like to deform?

This post imported from StackExchange MathOverflow at 2017-09-17 21:04 (UTC), posted by SE-user AHusain

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If you read German, try S. Waldmann's _ Poisson-Geometrie und Deformationsquantisierung. Eine Einführung._ (Springer, 2007).

This post imported from StackExchange MathOverflow at 2017-09-17 21:04 (UTC), posted by SE-user Igor Khavkine

Answer 1

Unfortunately, there is no real textbook on DQ around. One has Fedosov's book on his construction of star products including a detailed exposition of his index theorem.

There is a chapter on DQ in the recent Poisson geometry book by Laurent-Gengoux, Pichereau, Vanhaecke.

In the conference proceedings of the PQR2003 by Gutt, Rawnsley, and Sternheimer one finds some introductory texts, too.

Concerning the formality theorem of Kontsevich, one has the recent booklet by Esposito, which explains nicely the context (but does not contain the proof of the theorem)

You can also find lecture notes by Simone Gutt "Variations on DQ" or so, they should be on the arXiv somewhere, or on her homepage (?)

And, yes, as Igor mentioned, if you're not too afraid of german, then there is my german textbook on Poisson geometry and DQ with quite a bit of details.

This post imported from StackExchange MathOverflow at 2017-09-17 21:04 (UTC), posted by SE-user Stefan Waldmann

Answer 2

I realize this is a late answer, but in case there is still interest:
Michael Dütsch's recent book From Classical Field Theory to Perturbative Quantum Field Theory works with formal deformation quantization in causal perturbation theory and covers for example the Stueckelberg-Petermann renormalization group and QED. 

Comments

nice book!