Casimir Energies in Light of Quantum Field Theory

Noah Graham

Bicentennial Hall
Middlebury College
Middlebury, VT 05753

Traditional Casimir calculations are done by imposing perfect boundary conditions on surfaces. Of course, no real material creates a boundary condition at arbitrarily high energies; there is always an effective cutoff above which the material appears transparent. Although this idealization is justified in many useful problems, such the Casimir force between rigid bodies, there are situations where it can be hazardous, such as Casimir stress problems or general relativity applications. We present an efficient
calculational program in which we study the Casimir energy of a background potential that approximates a Dirichlet boundary condition. We conclude that the stress on the Dirichlet sphere depends on the details of the material that implements the cutoff, and thus is infinite in the limit of an
ideal boundary. This approach might also shed new light on the classic Boyer results for a conducting sphere.