Deformation quantization in FLRW geometries

TL;DR

This paper applies deformation quantization to analyze quantum and classical phase-space dynamics of a free particle in FLRW cosmological geometries, revealing curvature effects on quantum evolution.

Contribution

It introduces a semi-classical dynamical equation incorporating spatial curvature effects in FLRW universes using deformation quantization.

Findings

Curvature influences quantum phase-space evolution.

Derived a perturbative approach for spherically symmetric distributions.

Highlighted the role of deformation quantization in curved spacetime.

Abstract

We investigate the application of deformation quantization to the system of a free particle evolving within a universe described by a Friedmann-Lemaitre-Robertson-Walker (FLRW) geometry. This approach allows us to analyze the dynamics of classical and quantum phase-space distributions in curved spacetime. We demonstrate that when the curvature of the spatial sections is non-zero, the classical Liouville equation and its quantum counterpart, represented by the Moyal equation, exhibit distinct behaviors. Specifically, we derive a semi-classical dynamical equation that incorporates curvature effects and analyze the evolution of the Wigner quasi-distribution function in this cosmological context. By employing a perturbative approach, we elaborate on the case of a particle described by a spherically symmetric Wigner distribution and explore the implications for phase-space dynamics in expanding universes. Our findings provide new insights into the interplay between quantum mechanics, phase-space formulations, and cosmological expansion, highlighting the importance of deformation quantization techniques for understanding quantum systems in curved spacetime.