Quantization and scattering of massive scalar fields on exterior domains

A quantum theory is developed for the scattering of massive scalar fields on a class of non-globally hyperbolic spacetimes represented by foliations of Minkowski spacetime with a fixed compact set removed from each Cauchy surface. The field is restricted to the exterior of this set (exterior domain). At the classical level, the boundary value problem is recast as an abstract Cauchy problem in a Hilbert space, and the field solution is obtained as a unitary mapping of Cauchy data. The scattering theory is treated using a two Hilbert space approach, and the wave operators are constructed and shown to be asymptotically complete. At the quantum level, a field operator is constructed yielding a representation of the CCRs on a Fock space. Representations for the 'in' and 'out' asymptotic fields are developed, and a scattering operator is constructed and shown to be unitarily implementable. (author)