Orderings and non-formal deformation quantization

Hideki Omori, Yoshiaki Maeda, Naoya Miyazaki, Akira Yoshioka

    Research output: Contribution to journalArticlepeer-review

    16 Citations (Scopus)

    Abstract

    We propose suitable ideas for non-formal deformation quantization of Fréchet Poisson algebras. To deal with the convergence problem of deformation quantization, we employ Fréchet algebras originally given by Gel'fand-Shilov. Ideas from deformation quantization are applied to expressions of elements of abstract algebras, which leads to a notion of "independence of ordering principle". This principle is useful for the understanding of the star exponential functions and for the transcendental calculus in non-formal deformation quantization.

    Original languageEnglish
    Pages (from-to)153-175
    Number of pages23
    JournalLetters in Mathematical Physics
    Volume82
    Issue number2-3
    DOIs
    Publication statusPublished - 2007 Dec

    Keywords

    • Independence of ordering principle
    • Non-formal deformation quantization
    • Star exponential functions
    • Symbol calculus

    ASJC Scopus subject areas

    • Statistical and Nonlinear Physics
    • Mathematical Physics

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