A new nonformal noncommutative calculus: Associativity and finite part regularization

Hideki Omori, Yoshiaki Maeda, Naoya Miyazaki, Akira Yoshioka

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

We interpret the element 1/2ih (u * v + v * u) in the generators u, v of the Wey1 algebra W2 as an indeterminate in N+ 1/2 or -(N+ 1/2), using methods of the transcendental calculus outlined in the announcement [13]. The main purpose of this paper is to give a rigorous proof for the part of [13] which introduces this indeterminate phenomenon. Namely, we discuss how to obtain associativity in the transcendental calculus and show how the Hadamard finite part procedure can be implemented in our context.

Original languageEnglish
Title of host publicationDifferential Geometry, Mathematical Physics, Mathematics and Society Part 1
Pages267-297
Number of pages31
Edition321
Publication statusPublished - 2008 Oct 1
Externally publishedYes

Publication series

NameAsterisque
Number321
ISSN (Print)0303-1179

Keywords

  • Transcendental calculus
  • Weyl algebra

ASJC Scopus subject areas

  • Mathematics(all)

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  • Cite this

    Omori, H., Maeda, Y., Miyazaki, N., & Yoshioka, A. (2008). A new nonformal noncommutative calculus: Associativity and finite part regularization. In Differential Geometry, Mathematical Physics, Mathematics and Society Part 1 (321 ed., pp. 267-297). (Asterisque; No. 321).