  In this work we take a formal approach to the problem of decoupling Proca
equations in curved space-times. We use Newman-Penrose (NP) two-spinor
formalism to represent the Proca vector by one complex and two real scalars. We
show that a decoupled second order differential equation for one of the real
scalars can be derived if and only if the background space-time admits a
covariantly constant null vector. Thus, the background space-time must be a
pp-wave vacuum. We evaluate the separability of Proca, Maxwell and Dirac
equations on the resulting pp-wave background.
