Recent developments in deformation quantization
Stefan Waldmann
TL;DR
This paper reviews recent advances in deformation quantization, focusing on star products, their classification, and convergence issues, highlighting both mathematical structures and physical implications.
Contribution
It provides a comprehensive overview of recent developments in deformation quantization, emphasizing Morita classification and convergence problems.
Findings
Classification of star product algebras via Morita theory
Analysis of convergence leading to nuclear Weyl algebra
Integration of mathematical and physical perspectives
Abstract
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.
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Nonlinear Waves and Solitons