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

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 $\mathrm{\Theta }$, and an arbitrary symmetric matrix $\mathrm{\Phi }$, 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.