Quantum field theory with dynamical boundary conditions and the Casimir effect: Coherent states

TL;DR

This paper extends the analysis of a bulk-boundary quantum system with dynamical boundary conditions by introducing coherent states and examining their effects on Casimir energy and force, providing new insights into quantum boundary phenomena.

Contribution

It introduces coherent and thermal coherent states into a bulk-boundary quantum system with dynamical boundary conditions, extending previous work on Casimir effects.

Findings

Derived expressions for local polarization and Casimir energy in coherent states

Numerical results for Casimir energy and force in the extended framework

Enhanced understanding of quantum boundary effects with coherent states

Abstract

We have studied in a previous work the quantization of a mixed bulk-boundary system describing the coupled dynamics between a bulk quantum field confined to a spacetime with finite space slice and with timelike boundary, and a boundary observable defined on the boundary. Our bulk system is a quantum field in a spacetime with timelike boundary and a dynamical boundary condition-the boundary observable's equation of motion. Owing to important physical motivations, in such previous work we have computed the renormalized local state polarization and local Casimir energy for both the bulk quantum field and the boundary observable in the ground state and in a Gibbs state at finite, positive temperature. In this work, we introduce an appropriate notion of coherent and thermal coherent states for this mixed bulk-boundary system, and extend our previous study of the renormalized local state polarization and local Casimir energy to coherent and thermal coherent states. We also present numerical results for the integrated Casimir energy and for the Casimir force.