  New results for the fermion propagator in a laser background are presented.
We show that the all orders electron propagator can be written in a compact and
appealing form as a sum of sideband poles with a matrix wave function
renormalisation and a matrix valued mass shift. This last result is essential
in the fermionic theory if we are to maintain that both the mass and its square
pick up a correction only at order e^2. A perturbative verification of our
results is carried out.
