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Lechner, Gandalf; Waldmann, Stefan

Strict deformation quantization of locally convex algebras and modules. (English) Zbl 1330.53117

J. Geom. Phys. 99, 111-144 (2016).
Summary: In this work, various symbol spaces with values in a sequentially complete locally convex vector space are introduced and discussed. They are used to define vector-valued oscillatory integrals which allow to extend Rieffel’s strict deformation quantization to the framework of sequentially complete locally convex algebras and modules with separately continuous products and module structures, making use of polynomially bounded actions of \(\mathbb{R}^n\). Several well-known integral formulas for star products are shown to fit into this general setting, and a new class of examples involving compactly supported \(\mathbb{R}^n\)-actions on \(\mathbb{R}^n\) is constructed.

Cited in 8 Documents

MSC:

53D55 Deformation quantization, star products

Keywords:

locally convex algebra; deformation quantization; Rieffel construction; star product
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\textit{G. Lechner} and \textit{S. Waldmann}, J. Geom. Phys. 99, 111--144 (2016; Zbl 1330.53117)
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