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

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.