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Recent developments in deformation quantization. (English) Zbl 1338.81253

Finster, Felix (ed.) et al., Quantum mathematical physics. A bridge between mathematics and physics. Selected papers based on the presentations at the international conference, Regensburg, Germany, September 29 – October 2, 2014. Cham: Birkhäuser/Springer (ISBN 978-3-319-26900-9/hbk; 978-3-319-26902-3/ebook). 421-439 (2016).
Summary: In this review an overview on some recent developments in deformation quantization is given. After a general historical overview we motivate the basic definitions of star products and their equivalences both from a mathematical and a physical point of view. Then we focus on two topics: the Morita classification of star product algebras and convergence issues which lead to the nuclear Weyl algebra.
For the entire collection see [Zbl 1339.81008].

MSC:

81S10 Geometry and quantization, symplectic methods
53D55 Deformation quantization, star products
16D90 Module categories in associative algebras
46H05 General theory of topological algebras
46K05 General theory of topological algebras with involution
46A03 General theory of locally convex spaces
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