Strict deformation quantization of locally convex algebras and modules

JOURNAL OF GEOMETRY AND PHYSICS

卷:99

Article

Lechner, Gandalf¹  Waldmann, Stefan² 

[1] Cardiff Univ, Sch Math, Cardiff CF24 4AG, S Glam, Wales

[2] Univ Wurzburg, Lehrstuhl Math X, Inst Math, D-97074 Wurzburg, Germany

关键词: Locally convex algebra;    Deformation quantization;    Rieffel construction;    Star product;   

DOI  :  10.1016/j.geomphys.2015.09.013

来源: Elsevier

【 摘 要 】

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 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 R-n-actions on R-n is constructed. (C) 2015 Published by Elsevier B.V.

【 授权许可】

Free