Vector Coherent States from Plancherel's Theorem, Clifford Algebras and Matrix Domains

TL;DR

This paper introduces a generalized method for constructing vector coherent states using Plancherel's theorem, Clifford algebras, and matrix domains, expanding the framework beyond traditional scalar coherent states.

Contribution

It presents a novel technique for creating vector coherent states with finite or infinite components, applicable to groups, Clifford algebras, and matrix domains, including physical models.

Findings

Constructed vector coherent states via Plancherel isometry for groups.

Developed vector coherent states associated with Clifford algebras, including quaternions.

Applied the method to quantum optical models and matrix domains.

Abstract

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 in the same spirit. These vector coherent states may have a finite or an infinite number of components. As examples we first apply the technique to construct vector coherent states using the Plancherel isometry for groups and vector coherent states associated to Clifford algebras, in particular quaternions. As physical examples, we discuss vector coherent states for a quantum optical model and finally apply the general technique to build vector coherent states over certain matrix domains.