Deformation Expression for Elements of Algebras (III) --Generic product formula for *-exponentials of quadratic forms--

TL;DR

This paper introduces a generic product formula for *-exponentials of quadratic forms within the Weyl algebra, addressing the ordering problem in noncommutative algebra by providing a unified expression method.

Contribution

It presents a novel generic product formula for *-exponentials of quadratic forms in the Weyl algebra, advancing the understanding of element expression in noncommutative algebras.

Findings

Derived a product formula for Weyl algebra in generic ordered expression

Provided a unified approach to *-exponentials of quadratic forms

Addressed the ordering problem in noncommutative algebra

Abstract

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 give product formula of the Weyl algebra in generic ordered expression. In particular, the generic product formula of *-exponential functions of quadratic forms will be given.