  Electromagnetic and gravitational perturbations on Kerr spacetime can be
reconstructed from solutions to the Teukolsky equations. We study the canonical
quantization of solutions to these equations for any integer spin. Our
quantization scheme involves the analysis of the Hertz potential and one of the
Newman-Penrose scalars, which must be related via the Teukolsky-Starobinsky
identities. We show that the canonical commutation relations between the fields
can be implemented if and only if the Teukolsky-Starobinsky constants are
positive, which is the case both for gravitational perturbations and Maxwell
fields. We also obtain the Hadamard parametrix of the Teukolsky equation, which
is the basic ingredient for a local and covariant renormalization scheme for
non-linear observables. We also discuss the relation of the canonical energy of
Teukolsky fields to that of gravitational perturbations.
