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

Abstract

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.

References in corpus (2)

• Lectures on Special Lagrangian Submanifolds
• Deformation Expression for Elements of Algebras (I) --(Jacobi's theta functions and *-exponential functions)--

Cited by in corpus (6)

• Algebras with convergent star products and their representations in Hilbert spaces
• Deformation Expression for Elements of Algebras (III) --Generic product formula for *-exponentials of quadratic forms--
• Deformation Expression for Elements of Algebras (VI) --Vacuum representation of Heisenberg algebra--
• Deformation Expression for Elements of Algebras (V) - Diagonal matrix calculus and $\ast$-special functions -
• Deformation Expression for Elements of Algebras (VII) --Vacuum/Pseudo-vacuum Representations--
• Deformation Expression for Elements of Algebras (VIII) --SU(2)-vacuum and the regular representation space--