Deformation quantization in FLRW geometries
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866915069809393664 |
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| author | Bobadilla, Alfonso F. Cembranos, Jose A. R. |
| author_facet | Bobadilla, Alfonso F. Cembranos, Jose A. R. |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_13920 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Deformation quantization in FLRW geometries Bobadilla, Alfonso F. Cembranos, Jose A. R. General Relativity and Quantum Cosmology 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. |
| title | Deformation quantization in FLRW geometries |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2412.13920 |