GUP modified Wigner function using classical-quantum unified framework

Abstract

The generalized uncertainty principle (GUP) is a natural consequence of many proposed quantum gravity theories which further indicates the modification of the quantum mechanics and classical mechanics. A unified classical-quantum framework also leads to the interpretation of a Winger phase-space distribution of a state as a KvN wave function. In this article, we utilize the classical-quantum unified framework to calculate the expression for the GUP modified Wigner function of a classical harmonic oscillator in the configuration space instead of the conventional approach of utilising the momentum space. Further, we plot the modified Wigner functions and show that they are similar to what has been obtained before in the past literature.