SPECTRUM AND MASS OF PHOTON IN THE STATISTICAL QUANTUM ELECTRODYNAMICS

Aproximate solutions for the dispersion equations of the electromagnetic modes in the so called ''hot vacuum'' for two limit regions: omega = 0, k over arrow pointing right not-equal 0 and omega not-equal 0, k over arrow pointing right --> 0 are obtained. This is confirmed by comparying with the known exact asymptotic solutions. The propagation of the transversal and longitudinal modes are discussed for the mentioned regions. The dispersion curve for the transversal mode in the ''opaque'' region is found to be composed by two branches: the plasmonic branch, corresponding to massive quasi-particles, and the photonic one associated to massless particles. It is shown that the photonic distribution function has a divergent behavior for k over arrow pointing right --> 0 in the same way as in a massless gas, the infrared limit being omega = 0, k over arrow pointing right --> 0, and in the latter the number of quasi-particles is arbitrarly large. The analogy between this limit and the presence of a transversal condensate is shown. The comparison between the dispersion curve of the transverse mode of the black body at high temperature and the one for a charged boson gas with Bose-Einstein condensation is discussed. The relation between the phase transitions of symmetry restoration and Bose-Einstein condensation for massive vectorial fields with spontaneous symmetry breaking is established.