  We present a description of electrons propagating in an elliptically
polarised plane wave background which includes circular and linear
polarisations as special cases. We calculate to all orders in the background
field the two point function and relate it to various expressions found in the
literature. The background field induced mass shift of the electron is shown to
be polarisation independent in the full elliptic class. The matrix nature of
this mass shift in the fermionic theory is discussed. The extent to which a
momentum space description is possible for this system is clarified.
