Scattering operators on Fock space. I. Compact groups and internal symmetries

Abstract

The symmetric Fock space for a given representation of a compact internal symmetry group is shown to be naturally associated with an induced representation space, induced by a unitary group. The induced representation space is a Hilbert space over the complex sphere, and the orbits on this complex sphere with respect to the internal symmetry groups give rise to a double coset decomposition. A scattering operator acting on double coset representatives only is shown to be unitary, invariant with respect to the internal symmetry group, and include particle production. A simple example in which positively and negatively charged mesons generate a Fock space with respect to a U(1) internal symmetry group is given.