Casimir energy of Higgs-field configurations in a Coleman-Weinberg-type theory

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 lambdaphi/sup 4/ 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 formulas 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 or =5 are due to sharp boundaries of the configuration.