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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