Deformation Quantization: Observable Algebras, States and Representation Theory

Stefan Waldmann

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arXiv · hep-th/0303080

Deformation Quantization: Observable Algebras, States and Representation Theory

Stefan Waldmann

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Abstract

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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Stefan Waldmann. 2003-03-10. Deformation Quantization: Observable Algebras, States and Representation Theory. https://arxiv.org/abs/hep-th/0303080

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