Contact Geometry of Relativistic Particle Motion
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866913029646450688 |
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| author | Atesli, Begum Esen, Ogul Pavelka, Michal |
| author_facet | Atesli, Begum Esen, Ogul Pavelka, Michal |
| contents | We introduce a new geometric framework for relativistic particle dynamics based on contact geometry and suitable for treating dissipative processes like particle decay. The dynamics is formulated on a nine--dimensional extended phase space consisting of four position coordinates, four momenta, and an additional variable (functioning as a geometric variant of the particle's proper time). In this setting, the evolution is generated by an evolution contact vector field with a contact Hamiltonian encoding the mass shell. By promoting the proper time to an independent variable, the relativistic Hamilton canonical equations are rewritten in a fully geometric form without having to identify the proper time with a parameter along the worldlines. This makes for instance the evolution of massless particles (photons) well-defined without the need of reparametrization. The framework is then applied to decaying particles. Finally, we formulate a covariant kinetic theory and show how decaying particles can be described geometrically in this framework, changing the entropy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_12402 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Contact Geometry of Relativistic Particle Motion Atesli, Begum Esen, Ogul Pavelka, Michal Mathematical Physics General Relativity and Quantum Cosmology We introduce a new geometric framework for relativistic particle dynamics based on contact geometry and suitable for treating dissipative processes like particle decay. The dynamics is formulated on a nine--dimensional extended phase space consisting of four position coordinates, four momenta, and an additional variable (functioning as a geometric variant of the particle's proper time). In this setting, the evolution is generated by an evolution contact vector field with a contact Hamiltonian encoding the mass shell. By promoting the proper time to an independent variable, the relativistic Hamilton canonical equations are rewritten in a fully geometric form without having to identify the proper time with a parameter along the worldlines. This makes for instance the evolution of massless particles (photons) well-defined without the need of reparametrization. The framework is then applied to decaying particles. Finally, we formulate a covariant kinetic theory and show how decaying particles can be described geometrically in this framework, changing the entropy. |
| title | Contact Geometry of Relativistic Particle Motion |
| topic | Mathematical Physics General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2604.12402 |