Particles in Loop Quantum Gravity formalism: a thermodynamical description

TL;DR

This paper explores the thermodynamical behavior of particles in Loop Quantum Gravity, deriving analytical results for massive and massless cases, revealing dependencies on a modified dispersion relation and the Riemann zeta function.

Contribution

It provides an analytical thermodynamical analysis of particles in Loop Quantum Gravity, highlighting the effects of mass and a modified dispersion relation on thermodynamic properties.

Findings

Thermodynamics depends on a modified dispersion relation.

Mass influences thermodynamical properties significantly.

Properties are linked to the Riemann zeta function.

Abstract

In this work, we analyse the thermodynamical behavior of massive and massless particles within Loop Quantum Gravity formalism. We investigate a modified dispersion relation which suffices to derive all our results of interest in an \textit{analytical} manner. Initially, we study the massive case where, in essence, we examine how the mass modifies the thermodynamical properties of the system. On the other hand, to the massless case, the thermodynamical system turns out to rely only on a specific thermal state quantity, the temperature. More so, the analysis of the spectral radiation, the equation of states, the mean energy, the entropy, and the heat capacity are provided as well for both cases. Finally, the thermodynamical properties of our particles under consideration depends on the Riemann zeta function $\xi(s)$.