Local Neumann semitransparent layers: resummation, pair production and duality

TL;DR

This paper investigates local semitransparent Neumann boundary conditions for quantum scalar fields, deriving an effective action, analyzing pair production under perturbations, and revealing a duality with Dirichlet boundary conditions.

Contribution

It introduces a regularized approach to Neumann boundary conditions, computes the effective action explicitly in four dimensions, and establishes a strong/weak duality with Dirichlet boundary conditions.

Findings

Explicit heat-kernel expression for the effective action in D=4.

Analysis of pair production under harmonic and Sauter pulse perturbations.

Proof of a strong/weak duality linking Neumann and Dirichlet boundary theories.

Abstract

We consider local semitransparent Neumann boundary conditions for a quantum scalar field as imposed by a quadratic coupling to a source localized on a flat codimension-one surface. Upon a proper regularization to give meaning to the interaction, we interpret the effective action as a theory in a first-quantized phase space. We compute the relevant heat-kernel to all order in a homogeneous background and to quadratic order in perturbations, giving a closed expression for the corresponding effective action in $D=4$. In the dynamical case, we analyze the pair production caused by a harmonic perturbation and by a Sauter pulse. Notably, we prove the existence of a strong/weak duality that links this Neumann field theory to the analogue Dirichlet one.