We evaluate the in-medium p meson self energy by utilizing the conventionalπ-p dynamics in the one loop order. We pay attention to the gauge invariance of the rho self energy and analyze its dependence on the invariant mass M and spatial momentum ∣p∣ of the p meson. We show that this dependence leads to the modification of the thermal dilepton production rate. The pole positions and the values of the imaginary parts of the self-energy for different polarization states have different functional dependence on M and ∣p∣, which leads to the perceptible asymmetry of the dieiectron production when the momentum t = p+ - p- is perpendicular or parallel to p.