Coherent states: Theory and some applications

TLDR

Coherent states enable a detailed exploration of the topological and algebraic structure of dynamical systems. This review presents a general algorithm for constructing coherent states of dynamical groups for a given quantum physical system. The algorithm constructs coherent states, builds a quantum‑mechanical phase‑space representation, and applies methods such as path integrals, variational principles, classical limits, and thermodynamic limits to study quantum‑dynamic phenomena. For any dynamical group, the resulting coherent states are isomorphic to a coset space of the group’s geometrical space.

Abstract

In this review, a general algorithm for constructing coherent states of dynamical groups for a given quantum physical system is presented. The result is that, for a given dynamical group, the coherent states are isomorphic to a coset space of group geometrical space. Thus the topological and algebraic structure of the coherent states as well as the associated dynamical system can be extensively discussed. In addition, a quantum-mechanical phase-space representation is constructed via the coherent-state theory. Several useful methods for employing the coherent states to study the physical phenomena of quantum-dynamic systems, such as the path integral, variational principle, classical limit, and thermodynamic limit of quantum mechanics, are described.