Fermionic dispersion relations at finite temperature and non-vanishing chemical potentials in the minimal standard model

We calculate the fermionic dispersion relations in the minimal standard model at finite temperature in presence of non-vanishing chemical potentials due to the CP-asymmetric fermionic background. The dispersion relations are calculated for a vacuum expectation value of the Higgs field equal to zero (unbroken electroweak symmetry). The calculation is performed in the real time formalism of the thermal field theory at one-loop order in a general $\xi$ gauge. The fermionic self-energy is calculated at leading order in temperature and chemical potential and this fact permits us to obtain gauge invariant analytical expressions for the dispersion relations.