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


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
Number of pages31
Publication statusPublished - 2008 Oct 1

Publication series

ISSN (Print)0303-1179


  • Transcendental calculus
  • Weyl algebra

ASJC Scopus subject areas

  • General Mathematics


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