Real-time propagators at finite temperature and chemical potential

We derive a form of spectral representations for all bosonic and fermionic propagators in the real-time formulation of field theory at finite temperature and chemical potential. Besides being simple and symmetrical between the bosonic and the fermionic types, these representations depend explicitly on analytic functions only. This last property allows a simple evaluation of loop integrals in the energy variables over propagators in this form, even in presence of chemical potentials, which is not possible over their conventional form.