  The classical dynamics and the construction of quantum states in a plane wave
curved spacetime are examined, paying particular attention to the similarities
with the case of an electromagnetic plane wave in flat spacetime. A natural map
connecting the dynamics of a particle in the Rosen metric and the motion of a
charged particle in an electromagnetic plane wave is unveiled. We then discuss
how this map can be translated into the quantum description by exploiting the
large number of underlying symmetries. We examine the complete analogy between
Volkov solutions and fermion states in the Rosen chart and properly extend this
to massive vector bosons. We finally report the squared S-matrix element of
Compton scattering in a sandwich plane wave spacetime in the form of a
two-dimensional integral.
