Dynamical Casimir effect in the worldline formulation

TL;DR

This paper uses the worldline formulation to evaluate the effective action for the Dynamical Casimir Effect in scalar fields, deriving systematic corrections and applying the method to complex geometries.

Contribution

It introduces a novel worldline approach to compute the DCE effective action, including corrections for imperfect boundary conditions and multi-surface configurations.

Findings

Recovered Dirichlet boundary condition results in strong coupling limit

Derived systematic inverse coupling corrections

Applied method to two-surface geometries

Abstract

We evaluate the effective action for the Dynamical Casimir Effect (DCE) for a real scalar field in d+1 dimensions within the worldline formulation of quantum field theory. The scalar field is coupled to a spacetime-dependent mass term, which here plays the role of the moving medium and imposes imperfect boundary conditions on time-dependent surfaces. Expanding in powers of the departure of the geometry from a planar configuration, the worldline path integral factorizes into simpler, lower-dimensional ones. In the limit of a strong coupling to the surface, we recover the Dirichlet result and derive the systematic corrections in inverse powers of the coupling. Finally, we also apply the method to a two-surface configuration.