Deformation Quantizations of the Poisson Algebra of Laurent Polynomials

Hideki Omori, Yoshiaki Maeda, Naoya Miyazaki, Akira Yoshioka

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

It is well known that the Moyal bracket gives a unique deformation quantization of the canonical phase space ℝ2n up to equivalence. In his presentation of an interesting deformation quantization of the Poisson algebra of Laurent polynomials, Ovsienko discusses the equivalences of deformation quantizations of these algebras. We show that under suitable conditions, deformation quantizations of this algebra are equivalent. Though Ovsienko showed that there exists a deformation quantization of the Poisson algebra of Laurent polynomials which is not equivalent to the Moyal product, this is not correct. We show this equivalence by two methods: a direct construction of the intertwiner via the star exponential and a more standard approach using Hochschild 2-cocycles.

Original languageEnglish
Pages (from-to)171-180
Number of pages10
JournalLetters in Mathematical Physics
Volume46
Issue number2
Publication statusPublished - 1998 Oct 2
Externally publishedYes

Fingerprint

Deformation Quantization
Poisson Algebra
Laurent Polynomials
polynomials
algebra
equivalence
Equivalence
Algebra
Brackets
Cocycle
brackets
Phase Space
Star
stars
products

Keywords

  • Deformation quantization
  • Poisson algebra

ASJC Scopus subject areas

  • Mathematical Physics
  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics

Cite this

Deformation Quantizations of the Poisson Algebra of Laurent Polynomials. / Omori, Hideki; Maeda, Yoshiaki; Miyazaki, Naoya; Yoshioka, Akira.

In: Letters in Mathematical Physics, Vol. 46, No. 2, 02.10.1998, p. 171-180.

Research output: Contribution to journalArticle

Omori, Hideki ; Maeda, Yoshiaki ; Miyazaki, Naoya ; Yoshioka, Akira. / Deformation Quantizations of the Poisson Algebra of Laurent Polynomials. In: Letters in Mathematical Physics. 1998 ; Vol. 46, No. 2. pp. 171-180.
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