Polarisation tensor and collective phenomena in the relativistic e+e- plasma

The analytic properties of the polarisation tensor in quantum electrodynamics at finite temperature and density are investigated with the use of spectral representation. The polarisation tensor is considered as a function of complex frequency qsup(o). Explicit formulae for this branch of the polarisation tensor, which determines the poles of the propagator on the second Riemann sheet, are given. These formulae are further used in the investigation of longitudinal collective modes with qsup(o) <|q|. In particular, the dispersion of the mode and its decay width are discussed for temperatures between 108 and 6 x 109 K. It turns out that the equations determining the collective modes have no solutions for wavelengths smaller than some minimum wavelength. (author)