Effective Actions, Boundaries and Precision Calculations of Casimir Energies

TL;DR

This paper calculates the leading boundary correction to the QED Lagrangian near a conducting surface, clarifying previous misunderstandings and aiding theoretical models involving brane-world scenarios with boundary-generated kinetic terms.

Contribution

It provides a precise computation of boundary contributions to Casimir energies in QED, resolving existing ambiguities and offering insights for brane-world physics.

Findings

Resolved a confusion in the literature regarding boundary corrections to Casimir energy.

Derived the leading effective boundary term in the QED Lagrangian with conducting surfaces.

Established a theoretical framework applicable to brane-world models with boundary kinetic terms.

Abstract

We perform the matching required to compute the leading effective boundary contribution to the QED lagrangian in the presence of a conducting surface, once the electron is integrated out. Our result resolves a confusion in the literature concerning the interpretation of the leading such correction to the Casimir energy. It also provides a useful theoretical laboratory for brane-world calculations in which kinetic terms are generated on the brane, since a lot is known about QED near boundaries.