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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

ONE-PARTICLE AND COLLECTIVE ELECTRON SPECTRA IN HOT AND DENSE QED AND THEIR GAUGE DEPENDENCE