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Advances in the Casimir Effect$
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Michael Bordag, Galina Leonidovna Klimchitskaya, Umar Mohideen, and Vladimir Mikhaylovich Mostepanenko

Print publication date: 2009

Print ISBN-13: 9780199238743

Published to Oxford Scholarship Online: September 2009

DOI: 10.1093/acprof:oso/9780199238743.001.0001

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Regularization and Renormalization of the Vacuum Energy

Regularization and Renormalization of the Vacuum Energy

Advances in the Casimir Effect

M. Bordag

G. L. Klimchitskaya

U. Mohideen

V. M. Mostepanenko

Oxford University Press

This chapter uses the method of heat kernel expansion together with cutoff regularization to separate the divergent part of the vacuum energy. After the vacuum energy has been regularized, the procedure of renormalization is considered. The divergent contributions have a structure which allows their removal by a redefinition of the parameters in the ‘noninteracting theory’ (including the parameters of a classical background field if one is present). However, this procedure is not always possible. In the case of background fields (if these are singular or if one uses some limiting process which makes them singular) these questions are not completely settled, and they are briefly discussed. The cases of a single body and two separate bodies are considered in detail.

Keywords:   heat kernel expansion, divergent part, renormalization, frequency cutoff, point splitting, zeta function regularization

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