Contact Geometry of Relativistic Particle Motion

Fuente: arXiv
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Main Authors: Atesli, Begum, Esen, Ogul, Pavelka, Michal
Format: Preprint
Published: 2026
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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