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
    DOIs
    Publication statusPublished - 1998 Oct 2

    Keywords

    • Deformation quantization
    • Poisson algebra

    ASJC Scopus subject areas

    • Statistical and Nonlinear Physics
    • Mathematical Physics

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