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

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.