A Renormalized perturbation theory for problems with nontrivial boundary conditions or backgrounds in two space-time dimensions

Abstract

In this paper we discuss the effects of nontrivial boundary conditions or backgrounds, including non-perturbative ones, on the renormalization program for systems in two dimensions. Here we present an alternative renormalization procedure such that these non-perturbative conditions can be taken into account in a self-contained and, we believe, self-consistent manner. These conditions have profound effects on the properties of the system, in particular all of its $n$-point functions. To be concrete, we investigate these effects in the $\lambda {\varphi }^4$ model in two dimensions and show that the mass counterterms turn out to be proportional to the Green's functions which have nontrivial position dependence in these cases. We then compute the difference between the mass counterterms in the presence and absence of these conditions. We find that in the case of nontrivial boundary conditions this difference is minimum between the boundaries and infinite on them. The minimum approaches zero when the boundaries go to infinity. In the case of nontrivial backgrounds, we consider the kink background and show that the difference is again small and localized around the kink.

7 pages, 2 figures, revtex4, submmited to Eur. Phys. J. C

References in corpus (9)

• Anomaly and quantum corrections to solitons in two-dimensional theories with minimal supersymmetry
• No saturation of the quantum Bogomolnyi bound by two-dimensional supersymmetric solitons
• Radiative corrections to the Casimir effect for the massive scalar field
• Finite Size Effects in the Anisotropic λ/4!(ϕ^4_1 + ϕ^4_2)_d Model
• Local Casimir Energy For Solitons
• The Dirichlet Casimir effect for ${\varphi }^4$ theory in (3+1) dimensions: A new renormalization approach
• A new renormalization approach to the Dirichlet Casimir effect for ϕ^4 theory in (1+1) dimensions
• The Two-loop Massless phi^4 Model in Non-translational Invariant Domain
• Finite Size Effects in Thermal Field Theory

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• Radiative Correction to the Casimir Energy for Lorentz-violating Scalar Field in d+1 Dimensions
• Coordinate space representation for renormalization of quantum electrodynamics
• One-Loop Correction to the Casimir Energy in Lorentz-Violating ${\varphi }^4$ Theory with Rough Membrane Boundaries
• A Renormalization Program for Systems with Non-Perturbative Conditions
• Casimir Energy for Lorentz-Violating Scalar Field with Helical Boundary Condition in d Spatial Dimensions