Covariant description of particle creation in curved spaces

Following a survey about Fock representations and Feyn-man's theory of antiparticles, a gauge-covariant definition of ingoing and outgoing scalar particles in an external field is proposed which employs the resolvents of the Klein-Gordon operator. When applied to external electromagnetic fields, this definition leads to particle creation where it is physically expected. Special gravitational fields are also treated and creation in de Sitter space predicted. Finally, it is pointed out that this approach yields the same vacuum persistence amplitude as the Schwinger deWitt formalism and that it attributes physical meaning to the introduction of a ''proper time'' parameter in the Klein-Gordon equation