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

2011/07/13 by Hideki Omori, Yoshiaki Maeda, Omori, Hideki +5
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.MP

paper · pdf · doi:10.48550/arxiv.1107.2474

arxiv created 2011/07/13 · openalex publication_date 2011/07/13 · arxiv updated 2011/07/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Deformation Expression for Elements of Algebras (I) --(Jacobi's theta functions and *-exponential functions)--

Related

• Deformation Expression for Elements of Algebras (II) --(Weyl algebra of 2m-generators)--
• Deformation Expression for Elements of Algebras (IV) --Matrix elements and related integrals--
• Deformation Expression for Elements of Algebras (I) --(Jacobi's theta functions and *-exponential functions)--
• Deformation Expression for Elements of Algebra
• Deformation Expression for Elements of Algebras (V) - Diagonal matrix calculus and *-special functions -