Orderings and non-formal deformation quantization

Hideki Omori, Yoshiaki Maeda, Naoya Miyazaki, Akira Yoshioka

    Research output: Contribution to journalArticle

    14 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 1

    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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    Omori, H., Maeda, Y., Miyazaki, N., & Yoshioka, A. (2007). Orderings and non-formal deformation quantization. Letters in Mathematical Physics, 82(2-3), 153-175. https://doi.org/10.1007/s11005-007-0208-5