Algebras with convergent star products and their representations in Hilbert spaces

Journal Article · Mon Jul 15 00:00:00 EDT 2013 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.4815996· OSTI ID:22218271

Soloviev, M. A. ^[1]

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1. I. E. Tamm Department of Theoretical Physics, P. N. Lebedev Physical Institute, Leninsky prospect 53, Moscow 119991 (Russian Federation)

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.

• OSTI ID: 22218271
• Journal Information: Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 7 Vol. 54; ISSN JMAPAQ; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ALGEBRA
ANALYTIC FUNCTIONS
COMMUTATION RELATIONS
DEFORMATION
HILBERT SPACE
POWER SERIES
QUANTIZATION
QUANTUM FIELD THEORY