Considerations of the duality in generalized coherent states formalism

TL;DR

This paper introduces dual operators and constructs dual pairs of generalized displacement operators, revealing that certain generalized coherent states are dual, and analyzes their properties comparatively.

Contribution

It presents a novel duality framework for generalized coherent states using dual operators and displacement operators, offering new insights into their characteristics.

Findings

Barut-Girardello and Klauder-Perelomov states are dual

Constructed characteristics of these coherent states

Compared properties of dual coherent states

Abstract

In the paper, a pair of dual operators is introduced with which a dual pair of generalized displacement operators is constructed. With these entities it is shown that the Barut - Girardello and Klauder - Perelomov generalized coherent states are dual states. The characteristics of these coherent states are constructed, separately and comparatively.