Finite Temperature behavior of the CPT-even and parity-even electrodynamics of the Standard Model Extension

TL;DR

This paper investigates the finite temperature behavior of Lorentz-violating CPT-even electrodynamics within the Standard Model Extension, revealing anisotropic black body radiation and modifications to the Stefan-Boltzmann constant.

Contribution

It provides a gauge-invariant partition function for the LIV electrodynamics and explicitly analyzes the parity-even sector, highlighting how LIV affects thermodynamic properties.

Findings

LIV induces anisotropy in black body radiation.

The Planck law's frequency dependence remains unchanged.

The Stefan-Boltzmann constant is modified by LIV contributions.

Abstract

In this work, we examine the finite temperature properties of the CPT-even and Lorentz-invariance-violating (LIV) electrodynamics of the standard model extension, represented by the term $W_{\alpha \nu \rho \phi}F^{\alpha \nu}F^{\rho \phi}$. We begin analyzing the hamiltonian structure following the Dirac's procedure for constrained systems and construct a well-defined and gauge invariant partition function in the functional integral formalism. Next, we specialize for the non-birefringent coefficients of the tensor $W_{\alpha \nu \rho \phi}$. In the sequel, the partition function is explicitly carried out for the parity-even sector of the tensor $W_{\alpha \nu \rho \phi}$. The modified partition function is a power of the Maxwell's partition function. It is observed that the LIV coefficients induce an anisotropy in the black body angular energy density distribution. The Planck's radiation law, however, retains its frequency dependence and the Stefan-Boltzmann law keeps the usual form, except for a change in the Stefan-Boltzmann constant by a factor containing the LIV contributions.