  We investigate linearized gauge theories on globally hyperbolic spacetimes in
the BRST formalism. A consistent definition of the classical phase space and of
its Cauchy surface analogue is proposed. We prove that it is isomorphic to the
phase space in the subsidiary condition approach of Hack and Schenkel in the
case of Maxwell, Yang-Mills, and Rarita-Schwinger fields. Defining Hadamard
states in the BRST formalism in a standard way, their existence in the Maxwell
and Yang-Mills case is concluded from known results in the subsidiary condition
(or Gupta-Bleuler) formalism. Within our framework, we also formulate criteria
for non-degeneracy of the phase space in terms of BRST cohomology and discuss
special cases. These include an example in the Yang-Mills case, where
degeneracy is not related to a non-trivial topology of the Cauchy surface.
