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arXiv · 2604.12402

Contact Geometry of Relativistic Particle Motion

Begum Atesli·Ogul Esen·Michal Pavelka
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Abstract

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.

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Begum Atesli, Ogul Esen, Michal Pavelka. 2026-04-14. Contact Geometry of Relativistic Particle Motion. https://arxiv.org/abs/2604.12402

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