Geodesic equation in noncommutative space: a field theory perspective
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866910033762058240 |
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| author | Gregory, Carolina Matté Jurić, Tajron Pinzul, Aleksandr |
| author_facet | Gregory, Carolina Matté Jurić, Tajron Pinzul, Aleksandr |
| contents | We derive the geodesic equation for point particles propagating in Moyal-type noncommutative spacetimes using a field-theoretic approach based on the quasi-classical limit of the noncommutative Klein-Gordon equation. Starting from a twisted-geometric construction of the covariant Laplace-Beltrami operator, we obtain the noncommutative Hamilton-Jacobi equation and show that all noncommutative effects are absorbed into an effective, position-dependent mass function $M(x)$ appearing in an otherwise standard relativistic dispersion relation. The corresponding particle dynamics then acquires an additional term in the geodesic equation that takes the form of a fixed external force $F_{\text{NC}}^μ= -\frac{1}{2} g^{μν}\partial_νM^2(x)$, sourced entirely by the quantum nature of spacetime. We compute this effective mass perturbatively up to fourth order in the noncommutativity parameter for a general metric, proving that all odd-order corrections vanish identically. For the specific case of an $(r-θ)$ twist applied to spherically symmetric backgrounds, we obtain explicit expressions demonstrating that the leading correction to geodesic motion appears at $Θ^2$ order and is proportional to the probe particle's mass, while massless particles remain unaffected. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_22726 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Geodesic equation in noncommutative space: a field theory perspective Gregory, Carolina Matté Jurić, Tajron Pinzul, Aleksandr High Energy Physics - Theory General Relativity and Quantum Cosmology We derive the geodesic equation for point particles propagating in Moyal-type noncommutative spacetimes using a field-theoretic approach based on the quasi-classical limit of the noncommutative Klein-Gordon equation. Starting from a twisted-geometric construction of the covariant Laplace-Beltrami operator, we obtain the noncommutative Hamilton-Jacobi equation and show that all noncommutative effects are absorbed into an effective, position-dependent mass function $M(x)$ appearing in an otherwise standard relativistic dispersion relation. The corresponding particle dynamics then acquires an additional term in the geodesic equation that takes the form of a fixed external force $F_{\text{NC}}^μ= -\frac{1}{2} g^{μν}\partial_νM^2(x)$, sourced entirely by the quantum nature of spacetime. We compute this effective mass perturbatively up to fourth order in the noncommutativity parameter for a general metric, proving that all odd-order corrections vanish identically. For the specific case of an $(r-θ)$ twist applied to spherically symmetric backgrounds, we obtain explicit expressions demonstrating that the leading correction to geodesic motion appears at $Θ^2$ order and is proportional to the probe particle's mass, while massless particles remain unaffected. |
| title | Geodesic equation in noncommutative space: a field theory perspective |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2602.22726 |