  Application of the so-called refined algebraic quantization scheme for
constrained systems to the relativistic particle provides an inner product that
defines a unique Fock representation for a scalar field in curved space-time.
The construction can be made rigorous for a general globally hyperbolic
space-time, but the quasifree state so obtained turns out to be unphysical in
general. We exhibit a closely related pair of Fock representations that is also
defined generically and conforms to the notion of in- and outgoing states in
those situations where particle creation by the external field is expected.
