Regularization dependence of vacuum energy in arbitrarily shaped cavities

The vacuum energy for a free scalar field in the case of an arbitrarily shaped cavity is discussed. A complete analysis of the divergences is presented and some regularization schemes are analyzed in some detail. The vacuum energy for a free scalar field defined on an ultrastatic three‐dimensional s...

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Bibliographic Details
Published in:Journal of mathematical physics 1992-01, Vol.33 (1), p.222-228
Main Authors: Cognola, Guido, Vanzo, Luciano, Zerbini, Sergio
Format: Article
Language:English
Subjects:
661320 - Auroral, Ionospheric, & Magnetospheric Phenomena- (1992-)
BAG MODEL
BOUNDARY CONDITIONS
BOUNDARY-VALUE PROBLEMS
CASIMIR EFFECT
CAVITIES
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
COMPOSITE MODELS
DIRICHLET PROBLEM
Exact sciences and technology
EXTENDED PARTICLE MODEL
Function theory, analysis
MANY-DIMENSIONAL CALCULATIONS
Mathematical methods in physics
MATHEMATICAL MODELS
MATHEMATICAL SPACE
METRICS
MINKOWSKI SPACE
PARTICLE MODELS
Physics
QUARK MODEL
SCALAR FIELDS
SPACE
SPACE-TIME
VACUUM STATES
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Summary:The vacuum energy for a free scalar field in the case of an arbitrarily shaped cavity is discussed. A complete analysis of the divergences is presented and some regularization schemes are analyzed in some detail. The vacuum energy for a free scalar field defined on an ultrastatic three‐dimensional space‐time R×S, S being a compact Riemann surface of genus greater than unity, is explicitly computed using the Selberg trace formula. As a result, a negative vacuum energy is found.
ISSN:0022-2488
1089-7658
DOI:10.1063/1.529948