Casimir, Energy of Higgs Field Configurations in a Coleman-weinberg-type Tmeory*

.?? The Casimir energy, the quantum correction part of the energy, of a class of space-dependent scalar field configurations is examined in a Coleman-Weinberg type Xd4-theory in the d-dimensional regularization scheme. For the cases when the scalar ) field is dependent on only one space-coordinate and partially excludes its fluctuations from a region of space, we develop formulae effective for evaluating the full one-loop Casimir energy. As an application, we evaluate a simple case and find that the Casimir energy yields the familiar quantum correction to the volume energy, an extra surface energy whose coefficient is finite for d 5 4, and a finite, exponentially small attractive term. It is shown that the divergences for d 2 5 are due to sharp boundaries of the configuration. Submitted to Physical Review D * Work supported by the Department of Energy, contract DEACO3-76SF00515.