The strong-coupling expansion and the ultra-local approximation in field theory

N.F. Svaiter

Physica A: Statistical Mechanics and its Applications, 2005, vol. 345, issue 3, 517-537

Abstract: We first discuss the strong-coupling expansion in (λϕ4)d theory and quantum electrodynamics in a d-dimensional Euclidean space. In a formal representation for the Schwinger functional, we treat the Gaussian part of the action as a perturbation with respect to the remaining terms. In this way, we develop a perturbative expansion around the ultra-local model, where fields defined at different points of Euclidean space are decoupled. We examine the singularities of the strong-coupling perturbative expansion, analysing the analytic structure of the zero-dimensional generating functions in the coupling constant complex planes. We also discuss the ultra-local generating functional in a non-polynomial model in field theory, defined by the following interaction Lagrangian density: LII(g1,g2;ϕ)=g1(cosh(g2ϕ(x))-1). Finally, we use the strong-coupling perturbative expansion to compute the renormalized vacuum energy of the strongly coupled (λϕ4)d theory, assuming that the scalar field is defined in a region bounded by two parallel hyperplanes, where we are imposing Dirichlet–Dirichlet boundary conditions.

Keywords: Strong coupling; Ultra-local; Vacuum energy (search for similar items in EconPapers)
Date: 2005
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:345:y:2005:i:3:p:517-537

DOI: 10.1016/j.physa.2004.06.164

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