Variational Approach to Gaussian Approximate Coherent States: Quantum Mechanics and Minisuperspace Field Theory

TL;DR

This paper develops a variational Hamiltonian approach to study the evolution and stability of Gaussian coherent states in quantum mechanics and minisuperspace field theory, demonstrating stability in a $ ext{λ} ext{ϕ}^4$ model.

Contribution

It introduces a novel variational method for analyzing coherent state dynamics and stability in both quantum mechanics and minisuperspace field theories.

Findings

Coherent states evolve according to a Hamiltonian parameter approach.

Homogeneous minisuperspace solutions are stable for positive parameters.

Rigorous stability results are obtained using KAM-type theorems.

Abstract

This paper has a dual purpose. One aim is to study the evolution of coherent states in ordinary quantum mechanics. This is done by means of a Hamiltonian approach to the evolution of the parameters that define the state. The stability of the solutions is studied. The second aim is to apply these techniques to the study of the stability of minisuperspace solutions in field theory. For a $\lambda \varphi^4$ theory we show, both by means of perturbation theory and rigorously by means of theorems of the K.A.M. type, that the homogeneous minisuperspace sector is indeed stable for positive values of the parameters that define the field theory.