On the Manifestly Covariant Juttner Distribution and Equipartition Theorem
Guillermo Chacon-Acosta, Leonardo Dagdug, Hugo A. Morales-Tecotl

TL;DR
This paper derives a manifestly covariant form of the Juttner distribution and equipartition theorem, establishing invariant temperature in relativistic kinetic theory using a new approach with Cartesian coordinates in momentum space.
Contribution
It presents a new derivation of the covariant Juttner distribution and equipartition theorem, emphasizing invariant temperature from manifest covariance and using Cartesian coordinates in momentum space.
Findings
Derived a covariant form of Juttner distribution.
Established invariant temperature from covariance principles.
Proposed a new covariant equipartition theorem.
Abstract
The relativistic equilibrium velocity distribution plays a key role in describing several high-energy and astrophysical effects. Recently, computer simulations favored Juttner's as the relativistic generalization of Maxwell's distribution for d=1,2,3 spatial dimensions and pointed to an invariant temperature. In this work we argue an invariant temperature naturally follows from manifest covariance. We present a new derivation of the manifestly covariant Juttner's distribution and Equipartition Theorem. The standard procedure to get the equilibrium distribution as a solution of the relativistic Boltzmann's equation is here adopted. However, contrary to previous analysis, we use cartesian coordinates in d+1 momentum space, with d spatial components. The use of the multiplication theorem of Bessel functions turns crucial to regain the known invariant form of Juttner's distribution. Since…
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