Propriedades termodinâmicas do campo eletromagnético no setor CPT-ımpar do modelo padrão estendido

Abstract

In this work we study the effects of the spontaneous breaking of Lorentz symmetry on black body radiation phenomenon in the context of the Maxwell-Caroll-Field-Jackiw (MCFJ) model. The MCFJ model is the electromagnetic CPT-odd sector of the standard model extension and, it presents for a purely space-like background a positive-definite hamiltonian. Firstly, we study the Maxwell electrodynamics by analyzing its hamiltonian structure following the Dirac s procedure for constrained systems. Then, we calculate the partition function via the path integrals formalism and consequently we obtain its thermodynamic properties such as: energy density, radiation pressure and the entropy. Afterwards, we apply the same procedure to find the partition function of the MCFJ model and we observe how the spectrum of black body changes due to the breaking of the CPT and Lorentz symmetries. We show that if the cosmic microwave background (CMB) radiation is described by this model, it shows an angular anisotropy in the energy density distribution. We also give, at leading order in the Lorentz violating parameter, the contributions of the Lorentz breaking for the Planck s radiation and the Stefan-Boltzmann laws. The Lorentz-violating (LV) corrections for the Planck s law is non-linear in the frequency and for the Stefan-Boltzmann law is quadratic in the temperature. Using our results, we set upper limits for the LV parameter by analyzing the Stefan-Boltmann law and the CMB anisotropy but it is shown that they are much less stringents that those obtained by birefringence or polarization analysis of light.