Casimir Energy for a Wedge with Three Surfaces and for a Pyramidal Cavity

TL;DR

This paper calculates the Casimir energy for a conformally coupled massless scalar field in geometries involving a wedge with three surfaces and a pyramidal cavity, using reflection groups to formulate Green functions.

Contribution

It introduces a method to compute Casimir energies in complex geometries like wedges and pyramids using reflection group techniques.

Findings

Explicit Casimir energy expressions for wedge and pyramidal geometries.

Application of reflection groups to Green function formulation.

Enhanced understanding of quantum field behavior in polyhedral cavities.

Abstract

Casimir energy calculations for the conformally coupled massless scalar field for a wedge defined by three intersecting planes and for a pyramid with four triangular surfaces are presented. The group generated by reflections are employed in the formulation of the required Green functions and the wave functions.