We study the behavior of the dynamical fermion mass when infrared divergences and mass shell singularities are present in a gauge theory. In particular, in the massive Schwinger model in covariant gauges we find that the pole of the fermion propagato
r is divergent and gauge dependent at one loop, but the leading singularities cancel in the quenched rainbow approximation. On the other hand, in physical gauges, we find that the dynamical fermion mass is finite and gauge independent at least up to one loop.
We study the question of stability of the ground state of a scalar theory which is a generalization of the phi^3 theory and has some similarity to gravity with a cosmological constant. We show that the ground state of the theory at zero temperature b
ecomes unstable above a certain critical temperature, which is evaluated in closed form at high temperature.
Combining the thermal operator representation with the dispersion relation in QED at finite temperature and chemical potential, we determine the complete retarded photon self-energy only from its absorptive part at zero temperature. As an application
of this method, we show that, even for the case of a nonzero chemical potential, the temperature dependent part of the one loop retarded photon self-energy vanishes in $(1+1)$ dimensional massless QED.
