Deformation Quantization: Observable Algebras, States and Representation Theory

Details Deformation Quantization: Observable Algebras, States and Representation Theory Deformation Quantization: Observable Algebras, States and Representation Theory

2003-03-10

arxiv.org/abs/hep-th/0303080v1

Physics

High Energy Physics

High Energy Physics - Theory

LaTeX2e, 32 pages. Lecture notes for the Kopaonik summer school 2002

Scientific paper

In these lecture notes I give an introduction to deformation quantization. The quantization problem is discussed in some detail thereby motivating the notion of star products. Starting from a deformed observable algebra, i.e. the star product algebra, physical applications require to study representations of this algebra. I review the recent development of a representation theory including techniques like Rieffel induction and Morita equivalence. Applications beyond quantization theory are found in noncommutative field theories.

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