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The Dirichlet Casimir effect for theory in (3+1) dimensions: A new renormalization approach
We calculate the next to the leading order Casimir effect for a real scalar
field, within theory, confined between two parallel plates in three
spatial dimensions with the Dirichlet boundary condition. In this paper we
introduce a systematic perturbation expansion in which the counterterms
automatically turn out to be consistent with the boundary conditions. This will
inevitably lead to nontrivial position dependence for physical quantities, as a
manifestation of the breaking of the translational invariance. This is in
contrast to the usual usage of the counterterms in problems with nontrivial
boundary conditions, which are either completely derived from the free cases or
at most supplemented with the addition of counterterms only at the boundaries.
Our results for the massive and massless cases are different from those
reported elsewhere. Secondly, and probably less importantly, we use a
supplementary renormalization procedure, which makes the usage of any analytic
continuation techniques unnecessary.Comment: JHEP3 format,20 pages, 2 figures, to appear in JHE