Waldmann, Stefan 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]. Cited in 6 Documents 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 Keywords:star products; deformation quantization; Morita classification; Weyl algebra PDF BibTeX XML Cite \textit{S. Waldmann}, in: 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. 421--439 (2016; Zbl 1338.81253) Full Text: DOI arXiv OpenURL References: This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.