Deformation quantization in FLRW geometries
Abstract 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 cu...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2025-05-01
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| Series: | European Physical Journal C: Particles and Fields |
| Online Access: | https://doi.org/10.1140/epjc/s10052-025-14197-8 |
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| Summary: | Abstract 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. |
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| ISSN: | 1434-6052 |