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  Deformation Quantization

+ 3 like - 0 dislike

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
asked May 13, 2016 in Theoretical Physics by satyendra (15 points) [ no revision ]
retagged Sep 17, 2017
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
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

2 Answers

+ 7 like - 0 dislike

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
answered May 13, 2016 by Stefan Waldmann (440 points) [ no revision ]
+ 2 like - 0 dislike

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. 

answered Aug 30, 2020 by anonymous [ no revision ]

nice book!

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