On Coherent States and q-Deformed Algebras

TL;DR

This paper explores the relationship between coherent states and q-deformed algebras, introducing new properties and formalisms to study q-classical mechanics, geometry, and complex realizations of quantum algebras.

Contribution

It provides a new path integral formalism and geometric insights into q-deformed coherent states and their applications.

Findings

Developed a path integral formalism for q-coherent states

Analyzed geometrical consequences of q-deformation

Constructed Bargmann complex analytic realizations

Abstract

We review some aspects of the relation between ordinary coherent states and q-deformed generalized coherent states with some of the simplest cases of quantum Lie algebras. In particular, new properties of (q-)coherent states are utilized to provide a path integral formalism allowing to study a modified form of q-classical mechanics, to probe some geometrical consequences of the q-deformation and finally to construct Bargmann complex analytic realizations for some quantum algebras.