Deformation Expression for Elements of Algebras (II) --(Weyl algebra of 2m-generators)--

Hideki Omori, Yoshiaki Maeda, Naoya Miyazaki, Akira Yoshioka

Published 2011-05-06, updated 2012-02-10Version 2

This is a noncommutative version of the previous work entitled "Deformation Expression for Elements of Algebras (I)." In general in a noncommutative algebra, there is no canonical way to express elements in univalent way, which is often called "ordering problem". In this note we discuss this problem in the case of the Weyl algebra of 2m-generators. By fixing an expression, we extends Weyl algebra transcendentally. We treat *-exponential functions of linear forms, and quadratic forms of crossed symbol under generic expression parameters.