A new renormalization approach to the Dirichlet Casimir effect for ϕ^4 theory in (1+1) dimensions

Abstract

The next to the leading order Casimir effect for a real scalar field, within ${\varphi }^4$ theory, confined between two parallel plates is calculated in one spatial dimension. Here we use the Green's function with the Dirichlet boundary condition on both walls. 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. We obtain \emph{finite} results for the massive and massless cases, in sharp contrast to some of the other reported results. Secondly, and probably less importantly, we use a supplementary renormalization procedure in addition to the usual regularization and renormalization programs, which makes the usage of any analytic continuation techniques unnecessary.

arXiv commentrevtex4, 11 pages, 2 figures, to appear in Phys. Lett. B

References in corpus (35)

• New Developments in the Casimir Effect
• The Casimir effect: Recent controversies and progress
• Zeta Functions and the Casimir Energy
• Calculating Vacuum Energies in Renormalizable Quantum Field Theories: A New Approach to the Casimir Problem
• Casimir effect for a $D$-dimensional sphere
• The Dirichlet Casimir Problem
• Topological boundary conditions, the BPS bound, and elimination of ambiguities in the quantum mass of solitons
• Casimir Energies in Light of Quantum Field Theory
• Radiative Correction to the Casimir Force on a Sphere
• Casimir Effects in Renormalizable Quantum Field Theories
• Casimir Effect of Strongly Interacting Scalar Fields
• $O(\alpha )$ Radiative Correction to the Casimir Energy for Penetrable Mirrors
• Radiative Corrections to the Casimir Energy
• Hadronic Contributions to the Muon Lifetime
• Radiative corrections to the Casimir effect for the massive scalar field
• Calculating Casimir Energies in Renormalizable Quantum Field Theory
• Heavy Fermion Stabilization of Solitons in 1+1 Dimensions
• Generalized Zeta Functions and One-loop Corrections to Quantum Kink Masses
• One-loop correction to classical masses of quantum kink families
• Fermionic One-Loop Corrections to Soliton Energies in 1+1 Dimensions
• Radiative corrections to the Casimir energy and effective field theory
• Quantum corrections to mass and central charge of supersymmetric solitons
• Justification of the zeta function renormalization in rigid string model
• The anomaly in the central charge of the supersymmetric kink from dimensional regularization and reduction
• Mode regularization of the susy sphaleron and kink: zero modes and discrete gauge symmetry
• Effective Lagrangians for Scalar Fields and Finite Size Effects in Field Theory
• Finite Size Effects in the Anisotropic λ/4!(ϕ^4_1 + ϕ^4_2)_d Model
• The Dirichlet Casimir effect for ${\varphi }^4$ theory in (3+1) dimensions: A new renormalization approach
• Radius Stabilization by Two-Loop Casimir Energy
• Semi-classical mass of quantum k-component topological kinks
• The Two-loop Massless phi^4 Model in Non-translational Invariant Domain
• Finite Size Effects in Thermal Field Theory
• Radiative corrections to the Casimir force and effective field theories
• Boundary conditions at spatial infinity for fields in Casimir calculations
• Comment on `One Loop Renormalization of Soliton Quantum Mass Corrections in 1+1 Dimensional Scalar Field Theory Models' (Phys. Lett. B542 (2002) 282 [hep-th/0206047])

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