Matrix representation of the generalized Moyal algebra

TL;DR

This paper demonstrates that the generalized Moyal algebra can be naturally represented as a matrix algebra, leveraging the generalized Weyl quantization rule and the matrix representation of creation and destruction operators.

Contribution

It establishes a natural isomorphism between the generalized Moyal algebra and matrix algebra using Weyl quantization and operator representations.

Findings

The isomorphism between generalized Moyal and matrix algebra is derived naturally.

The approach connects Weyl quantization with matrix representations of operators.

Provides a foundation for matrix-based analysis of generalized Moyal structures.

Abstract

It is shown that the isomorphism between the generalized Moyal algebra and the matrix algebra follows in a natural manner from the generalized Weyl quantization rule and from the well known matrix representation of the destruction and creation operators.