The full CPT-even photon sector of the Standard Model Extension at finite temperature

TL;DR

This paper investigates the finite temperature properties of the CPT-even photon sector in the Standard Model Extension, revealing modifications to the radiation law and energy density due to Lorentz-violating terms, while leaving the equation of state unchanged.

Contribution

It provides a detailed Hamiltonian analysis and explicit calculation of the partition function for the CPT-even photon sector with Lorentz violation at finite temperature.

Findings

Modified frequency dependence in Planck's radiation law.

Adjusted total energy density due to Lorentz-violating coefficients.

Equation of state remains unaffected by the modifications.

Abstract

We study the finite temperature behavior of the CPT-even pure-photon sector of the Standard Model Extension, which is defined by the standard Maxwell Lagrangian plus the term $(k_F)_{\mu\nu\alpha\beta}F^{\mu\nu}F^{\alpha\beta}$. The Hamiltonian analysis is performed, from which the degrees of freedom and constraints of the theory are derived. We have explicitly calculated the partition function for an arbitrary configuration of the $(k_F)_{\mu\nu\alpha\beta}$ coefficients, to second order, and we have used it to obtain the thermodynamic properties of the modified photon sector. We find the correction to the frequency dependence in Planck's radiation law, and we identify that the total energy density is adjusted, relative to the standard scenario, by a global proportionality constant containing the Lorentz-violating contributions. Nevertheless, the equation of state is not affected by these modifications.