Lie Algebras and Generalized Thermal Coherent States

TL;DR

This paper develops an algebraic framework for generalized thermal coherent states using Thermofield Dynamics, applying it to $SU(2)$ and $SU(1,1)$ symmetries to analyze their quantum properties.

Contribution

It introduces a novel algebraic formulation for thermal coherent states based on Lie group coset spaces, extending previous methods to multi-mode systems.

Findings

Derived thermal coherent states and density operators for $SU(2)$ and $SU(1,1)$

Calculated thermal quantum Fidelity for these states

Analyzed thermal Wigner functions for the constructed states

Abstract

In this paper, we developed an algebraic formulation for the generalized thermal coherent states with a Thermofield Dynamics approach for multi-modes, based on coset space of Lie groups. In particular, we applied our construction on $SU(2)$ and $SU(1,1)$ symmetries and we obtain their thermal coherent states and density operator. We also calculate their thermal quantum Fidelity and thermal Wigner function.