Vector Coherent States with an Unbounded Inverse Frame Operator

TL;DR

This paper introduces a new class of vector coherent states constructed using hermitian matrices within the complex unit disc, with an example based on the SU(1,1) group, expanding the mathematical framework of coherent states.

Contribution

It develops a novel construction of vector coherent states in multiple copies of the unit disc, including an explicit example using the SU(1,1) group, addressing unbounded inverse frame operators.

Findings

Constructed vector coherent states in n-copies of the unit disc.

Provided an explicit example using the SU(1,1) group.

Extended the mathematical framework of coherent states.

Abstract

We present a class of vector coherent states in the domain $D\times D\times >....\times D$ (n-copies), where $D$ is the complex unit disc, using a specific class of hermitian matrices. Further, as an example, we build vector coherent states in the unit disc by considering the unit disc as the homogeneous space of the group SU(1,1).