Rigorous control of the non-perturbative corrections to the double expansion in g and g²ln(g) for the ϕ⁴₃-trajectory in the hierarchical approximation

1998/09/09 by Christian Wieczerkowski
Physics and Astronomy · #hep-lat

paper · pdf

published as Helv.Phys.Acta 72 (1999) 445-483 · 42 pages LaTeX2e

arxiv created 1998/09/09 · arxiv updated 2009/12/01

Abstract

We study the renormalization invariant trajectory of the ϕ⁴-perturbation of the free field fixed point in the hierarchical approximation. We parametrize it by a running ϕ⁴-coupling g with linear step β-function. We rigorously control the non-perturbative corrections to finite order approximants from double perturbation theory in g and g²ln(g). The construction uses a contraction mapping for the extended renormalization group composed of a hierarchical block spin transformation with a flow of g.

Related

• The renormalized ϕ⁴₄-trajectory by perturbation theory in a running coupling using partial differential equations
• The Hierarchical ϕ⁴ - Trajectory by Perturbation Theory in a Running Coupling and its Logarithm
• A Perturbative Improvement of the Hierarchical Approximation
• Non-Perturbative Aspects of Scalar Field theory
• Perturbation theory with unstable fundamental fields