GUP modified Wigner function using classical-quantum unified framework

The generalized uncertainty principle (GUP) is a natural consequence of many proposed quantum gravity theories that indicate the modification of quantum mechanics and classical mechanics. A unified classical quantum framework also leads to the interpretation of a Wigner 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 that uses the momentum space. Further, we plot the modified Wigner functions and show that they are similar to the results obtained in the past literature.