Thermal effects of a photon gas with a deformed Heisenberg algebra

TL;DR

This paper investigates how a minimal measurable length, derived from a covariant generalized uncertainty principle, affects the thermodynamics of a photon gas, leading to corrections in the Stefan-Boltzmann law at high temperatures.

Contribution

It introduces a GUP-deformed Maxwell invariant and computes quantum corrections to photon gas thermodynamics, revealing GUP-induced modifications to classical laws.

Findings

GUP causes corrections to the Stefan-Boltzmann law.

One- and two-loop quantum contributions are calculated.

GUP effects are significant at high temperatures.

Abstract

In this paper we have consider the thermodynamics of a photon gas subject to the presence of a minimal measurable length following from a covariant extension of the original generalized uncertainty principle (GUP). After establishing consistently a generalized dynamics, we define a GUP deformed Maxwell invariant which serves as the basis for our study. In order to highlight the GUP effects we compute the one- and two-loop order contribution to the partition function at the high-temperature limit. Afterwards, by computing the internal energy density we conclude that the additional terms can be seen as corrections $\delta\sigma_{\rm{gup}}$ to the Stefan-Boltzmann law due to GUP effects.