A General formulation of the Moyal and Voros products and its physical interpretation

TL;DR

This paper introduces a generalized star product unifying Moyal and Voros formulations, exploring its quantum mechanical implications and physical interpretation.

Contribution

It defines a new star product using matrices that generalizes Moyal and Voros products, providing a broader framework for quantum mechanics.

Findings

The generalized star product encompasses Moyal and Voros products as special cases.

It offers a new perspective on the physical interpretation of non-commutative quantum mechanics.

The formulation clarifies the physical meaning of different star products in quantum theory.

Abstract

A unifying perspective on the Moyal and Voros products and their physical meanings has been recently presented in the literature, where the Voros formulation admits a consistent physical interpretation. We define a star product $\star$, in terms of an antisymmetric fixed matrix $\Theta$, and an arbitrary symmetric matrix $\Phi$, that is a generalization of the Moyal and the Voros products. We discuss the quantum mechanics and the physical meaning of the generalized star product.