  The worldline formalism has previously been used for deriving compact master
formulas for the QED $N$ - photon amplitudes in vacuum, in a constant field and
in a plane-wave field. Here we carry this program one step further by deriving
master formulas for the scalar and spinor QED $N$-photon amplitudes in the
background of the "parallel" special case of a combined constant and plane-wave
field.
