Coherent States for the Deformed Algebras

TL;DR

This paper develops a unified method to construct coherent states for various deformed algebras, facilitating their application in physical problems by linking them to Lie algebras and deriving generalized coherent states.

Contribution

It introduces a general procedure to find coherent states for multiple deformed algebras, including quadratic, Higgs, and q-deformed types, and connects them to Lie algebra frameworks.

Findings

Constructed coherent states for non-compact deformed algebras.

Mapped deformed algebras to Lie algebras for state construction.

Derived generalized Perelomov coherent states.

Abstract

We provide a unified approach for finding the coherent states of various deformed algebras, including quadratic, Higgs and q-deformed algebras, which are relevant for many physical problems. For the non-compact cases, coherent states, which are the eigenstates of the respective annihilation operators, are constructed by finding the canonical conjugates of these operators. We give a general procedure to map these deformed algebras to appropriate Lie algebras. Generalized coherent states, in the Perelomov sense, follow from this construction.