f-oscillators deformation for Moyal algebras

TL;DR

This paper develops a q-deformed Wigner-Weyl-Moyal quantization framework using star-products, providing explicit Groenewold kernels for nonlinear q-oscillators and exploring their deformations for various nonlinear vibrations.

Contribution

It introduces a generalized star-product construction for q-deformed quantization and explicitly derives Groenewold kernels for nonlinear q-oscillators, expanding the understanding of deformation quantization.

Findings

Explicit Groenewold kernels for small nonlinearities

Extension of deformation to general nonlinear vibrations

Framework for q-deformed quantization of f-oscillators

Abstract

Using general construction of star-product the q-deformed Wigner-Weyl-Moyal quantization procedure is elaborated. The q-deformed Groenewold kernel determining the product of quantum observables is given in explicit form for small nonlinearities corresponding to nonlinear vibrations of classical and quantum q-oscillators. The deformations of Groenewold kernel related to general kinds of nonlinear vibrations described by f-oscillators are considered.