https://doi.org/10.1140/epjc/s10052-025-14197-8
Regular Article - Theoretical Physics
Deformation quantization in FLRW geometries
1
Departamento de Física Teórica, Facultad de Ciencias Físicas, Universidad Complutense de Madrid, Plaza de Ciencias 1, 28040, Madrid, Spain
2
Facultad de Ciencias Físicas, Institute of Particle and Cosmos Physics (IPARCOS), Universidad Complutense de Madrid, Plaza de Ciencias 1, 28040, Madrid, Spain
Received:
27
January
2025
Accepted:
17
April
2025
Published online:
11
May
2025
We investigate the application of deformation quantization to the system of a free particle evolving within a universe described by a Friedmann–Lemaître–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.
© The Author(s) 2025
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