Unnatural Acts: Unphysical Consequences of Imposing Boundary Conditions on Quantum Fields

TL;DR

Imposing Dirichlet boundary conditions on quantum fields via coupling to a static background leads to divergent Casimir energies that depend on physical cutoffs, raising questions about the physical consistency of such boundary conditions.

Contribution

This paper demonstrates that enforcing boundary conditions through coupling causes unphysical divergences in Casimir energy, challenging traditional assumptions in quantum field theory.

Findings

Casimir energy diverges when boundary conditions are imposed via coupling.

Divergences cannot be removed by standard renormalization.

Surface energies depend on physical cutoffs, unlike forces away from surfaces.

Abstract

I examine the effect of trying to impose a Dirichlet boundary condition on a scalar field by coupling it to a static background. The zero point -- or Casimir -- energy of the field diverges in the limit that the background forces the field to vanish. This divergence cannot be absorbed into a renormalization of the parameters of the theory. As a result, the Casimir energy of a surface on which a Dirichlet boundary condition is imposed, and other quantities like the surface tension, which are obtained by deforming the surface, depend on the physical cutoffs that characterize the coupling between the field and the matter on the surface. In contrast, the energy density away from the surface and forces between rigid surfaces are finite and independent of these complications