# Classical phase space and Hadamard states in the BRST formalism for gauge field theories on curved spacetime

July 30, 2014

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 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.

Keywords:

quantum field theory on curved spacetimes, gauge field theories