The Dirichlet Casimir effect for ϕ4theory in (3 + 1) dimensions: a new renormalization approach

2007/08/30 by Reza Moazzemi, Maryam Namdar, S. S. Gousheh +1 · 2 citations
Mathematics · Physics and Astronomy · #Analytic continuation #Boundary (topology) #Boundary value problem #Casimir effect #Classical mechanics #Cosmology and Gravitation Theories #Dirichlet boundary condition #Geometry #Massless particle #Mathematical analysis #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Perturbation theory (quantum mechanics) #Physics #Quantum #Quantum Electrodynamics and Casimir Effect #Quantum gravity #Quantum mechanics #Renormalization #Renormalization group #Scalar (mathematics) #Scalar field #Scalar field theory #Theoretical physics #hep-th

paper · pdf · doi:10.1088/1126-6708/2007/09/029

published as JHEP 0709:029,2007 · JHEP3 format,20 pages, 2 figures, to appear in JHEP

arxiv created 2007/08/30 · openalex publication_date 2007/09/06 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We calculate the next to the leading order Casimir effect for a real scalar field, within ϕ⁴ 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.

Citations

• One-loop corrections to classical masses of kink families
• Calculating Vacuum Energies in Renormalizable Quantum Field Theories: A New Approach to the Casimir Problem
• The Influence of Retardation on the London-van der Waals Forces
• Finite size effects in thermal field theory
• Quantum Electromagnetic Zero-Point Energy of a Conducting Spherical Shell and the Casimir Model for a Charged Particle
• New Developments in the Casimir Effect
• A course of modern analysis an introduction to the general theory of infinite processes and of analytic functions with an account of the principal transcendental functions
• The anomaly in the central charge of the supersymmetric kink from dimensional regularization and reduction
• The Casimir effect: Recent controversies and progress
• One loop renormalization of soliton quantum mass corrections in (1+1)-dimensional scalar field theory models
• Schrödinger representation and Casimir effect in renormalizable quantum field theory
• The generalized Abel-Plana formula with applications to Bessel functions and Casimir effect

Cited by

• The Casimir energy for scalar field with mixed boundary condition
• Radiative correction to the Casimir energy for Lorentz-violating scalar field in d + 1 dimensions