Phase states and coherent states for generalized Weyl-Heisenberg algebras

TL;DR

This paper develops phase and coherent states for a generalized Weyl-Heisenberg algebra, exploring their construction in finite and infinite-dimensional spaces, and introduces foundational concepts for further quantum algebra research.

Contribution

It introduces a systematic construction of phase and coherent states for a polynomial algebra generalizing Weyl-Heisenberg algebra, expanding the understanding of quantum states in this framework.

Findings

Defined phase and coherent states for the algebra

Analyzed states in finite and infinite-dimensional spaces

Laid groundwork for future quantum algebra studies

Abstract

This paper is concerned with the construction of phase operators, phase states, vector phase states, and coherent states for a generalized Weyl-Heisenberg algebra. This polynomial algebra (that depends on real parameters) is briefly described. The various states are defined on a finite- or infinite-dimensional space depending on the parameters. This report constitutes an introduction to three papers published by the authors in J. Phys. A [43 (2010) 115303 and 45 (2012) 244036] and J. Math. Phys. [52 (2011) 082101]. See these three papers for the relevant references.