A Special Relativistic Liouville Equation Exists

TL;DR

This paper confirms the existence of a special relativistic Liouville equation by deriving a Hamiltonian in 8N phase space through symmetry breaking, advancing the theoretical framework of relativistic statistical mechanics.

Contribution

It introduces a Hamiltonian formulation in 8N phase space that establishes the existence of a relativistic Liouville equation, filling a gap in relativistic statistical theory.

Findings

Derived Hamiltonian in 8N phase space.

Established the existence of a relativistic Liouville equation.

Broken reparametrization symmetry to define evolution.

Abstract

In a previous paper, the author asked the question "Does a Special Relativistic Liouville Equation Exist?'. In this paper, I give an affirmative answer. In 8N phase space, a Hamiltonian is derived by breaking the reparametrization symmetry of the single, Lorentz invariant, mathematical time introduced, which defines the evolution of all phase space variables.