Casimir energy of a scalar field with a space-dependent mass distribution |
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Authors: | Hideaki Aoyama |
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Affiliation: | Stanford Linear Accelerator Center, Stanfford University, Stanford, California 94305, USA |
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Abstract: | The Casimir energy is evaluated for a free scalar field that has a mass term m2(x1), depending on one space coordinate x1. The formalism for evaluating the Casimir energy is developed for the case of m2(x1) finite everywhere in d-dimensional space-time. The case with ) is explicity evaaluated for any value of 1197 1568 V m0 and m∞ without any approximation. The result consists of valume energy terms, a surface term, and a non-leading term. Most of the UV divergences are in the volume energy terms and renormalize the coupling constants of the underlying theory. The surface energy term is finite for d ? 4 and divergent for d ? 5 due to the boundaries being sharp. A closed finite expression is obtained for the non-leading term. Our results are shown to reproduce the known Casimir energies for the limiting cases, 1197 15 m0 → ∞ andm∞ → ∞. |
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