  The one-particle electron spectrum is found for hot and dense QED and its
properties are investigated in comparison with the collective spectrum. It is
shown that the one-particle spectrum (in any case its zero momentum limit) is
gauge invariant, but the collective spectrum, being qualitatively different, is
always gauge dependent. The exception is the case $m,\mu=0$ for which the
collective spectrum long wavelength limit demonstrates the gauge invariance as
well.
