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Title: Algebras with convergent star products and their representations in Hilbert spaces

We study star product algebras of analytic functions for which the power series defining the products converge absolutely. Such algebras arise naturally in deformation quantization theory and in noncommutative quantum field theory. We consider different star products in a unifying way and present results on the structure and basic properties of these algebras, which are useful for applications. Special attention is given to the Hilbert space representation of the algebras and to the exact description of their corresponding operator algebras.
Authors:
 [1]
  1. I. E. Tamm Department of Theoretical Physics, P. N. Lebedev Physical Institute, Leninsky prospect 53, Moscow 119991 (Russian Federation)
Publication Date:
OSTI Identifier:
22218271
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 54; Journal Issue: 7; Other Information: (c) 2013 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; ALGEBRA; ANALYTIC FUNCTIONS; COMMUTATION RELATIONS; DEFORMATION; HILBERT SPACE; POWER SERIES; QUANTIZATION; QUANTUM FIELD THEORY