Self-energy of the electron at high density

The electron self-energy is examined at high density. An analytic expression for it is obtained at zero temperature in the lowest order of perturbation theory. Using this expression, a real and gauge-invariant dispersion relation is obtained. Consequently the mass shift remains real in this order. The application of these results to neutron and quark stars is briefly discussed. Finally, the validity of the one-loop approximation is also examined. (orig.)