Divergences in the vacuum energy for frequency-dependent interactions

TL;DR

The paper introduces a method to identify ultra-violet divergences in vacuum energy for systems with frequency-dependent spectra, applied to plasma shell models interacting with electromagnetic fields.

Contribution

It presents a novel approach for calculating divergences in systems with non-linear spectral problems, specifically applied to plasma shell models with curvature considerations.

Findings

Divergences expressed as surface integrals of invariants

Method applicable to frequency-dependent fluctuation operators

Analysis of slightly curved plasma sheets

Abstract

We propose a method for determining ultra-violet divergences in the vacuum energy for systems whose spectrum of perturbations is defined through a non-linear spectrum problem, i.e, when the fluctuation operator itself depends on the frequency. The method is applied to the plasma shell model, which describes some properties of the interaction of electromagnetic field with fullerens. We formulate a scalar model, which simplifies the matrix structure, but keeps the frequency dependence of the plasma shell, and calculate the ultra-violet divergences in the case when the plasma sheet is slightly curved. The divergent terms are expressed in terms of surface integrals of corresponding invariants.