Hamiltonian approach to the dynamical Casimir effect

TL;DR

This paper introduces a Hamiltonian method to analyze the dynamical Casimir effect, addressing key issues in physical description, ensuring positive energy particles, and maintaining energy conservation during mirror motion.

Contribution

A novel Hamiltonian framework for the dynamical Casimir effect that resolves previous problems and can be extended to various fields and dimensions.

Findings

The reactive term proportional to mirror acceleration is essential for positive energy particles.

The approach ensures energy conservation during mirror movement.

Comparison with previous methods clarifies their interrelations.

Abstract

A Hamiltonian approach is introduced in order to address some severe problems associated with the physical description of the dynamical Casimir effect at all times. For simplicity, the case of a neutral scalar field in a one-dimensional cavity with partially transmitting mirrors (an essential proviso) is considered, but the method can be extended to fields of any kind and higher dimensions. The motional force calculated in our approach contains a reactive term --proportional to the mirrors' acceleration-- which is fundamental in order to obtain (quasi)particles with a positive energy all the time during the movement of the mirrors --while always satisfying the energy conservation law. Comparisons with other approaches and a careful analysis of the interrelations among the different results previously obtained in the literature are carried out.