The Dirichlet Casimir effect for $φ^4$ theory in 3 1 dimensions: A new renormalization approach - High Energy Physics - TheoryReport as inadecuate




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Abstract: We calculate the next to the leading order Casimir effect for a real scalarfield, within $\phi^4$ theory, confined between two parallel plates in threespatial dimensions with the Dirichlet boundary condition. In this paper weintroduce a systematic perturbation expansion in which the countertermsautomatically turn out to be consistent with the boundary conditions. This willinevitably lead to nontrivial position dependence for physical quantities, as amanifestation of the breaking of the translational invariance. This is incontrast to the usual usage of the counterterms in problems with nontrivialboundary conditions, which are either completely derived from the free cases orat most supplemented with the addition of counterterms only at the boundaries.Our results for the massive and massless cases are different from thosereported elsewhere. Secondly, and probably less importantly, we use asupplementary renormalization procedure, which makes the usage of any analyticcontinuation techniques unnecessary.



Author: Reza Moazzemi, Maryam Namdar, Siamak S. Gousheh

Source: https://arxiv.org/







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