Vector coherent states from Plancherel's theorem, Clifford algebras and matrix domains

As a substantial generalization of the technique for constructing canonical and the related nonlinear and q-deformed coherent states, we present here a method for constructing vector coherent states (VCS) in the same spirit. These VCS may have a finite or an infinite number of components. The resulting formalism, which involves an assumption on the existence of a resolution of the identity, is broad enough to include all the definitions of coherent states existing in the current literature, subject to this restriction. As examples, we first apply the technique to construct VCS using the Plancherel isometry for groups and VCS associated with Clifford algebras, in particular quaternions. As physical examples, we discuss VCS for a quantum optical model and finally apply the general technique to build VCS over certain matrix domains