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].

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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\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)