  In this work we report new results concerning the question of dynamical mass
generation in the Lorentz and PCT violating quantum electrodynamics. A one loop
calculation for the vacuum polarization tensor is presented. The electron
propagator, "dressed" by a Lorentz breaking extra term in the fermion
Lagrangian density, is approximated by its first order: this scheme is shown to
break gauge invariance. Then we rather consider a full calculation to second
order in the Lorentz breaking parameter: we recover gauge invariance and use
the Schwinger-Dyson equation to discuss the full photon propagator. This allows
a discussion on a possible photon mass shift as well as measurable, observable
physical consequences, such as the Lamb-shift.
