Algebraic Solution for a Dirac Electron in a Plane-Wave Electromagnetic Field

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Abstract
An algebraic classification is given for the solutions of the Dirac equation for an electron interacting with a classical plane‐wave electromagnetic field. The solutions appear as the carrier space of the direct sum of the positive and negative energy, mass m, spin‐½ representations of the restricted Poincaré group. An explicit construction is given for the generators of the representation. The explicit position space form of the solutions follows readily from the relatively simple form of these operators. Via these solutions, an expression for the propagator of the interacting electron is given.