English

A method for resummation of perturbative series based on the stochastic solution of Schwinger-Dyson equations

High Energy Physics - Lattice 2011-09-19 v2 Statistical Mechanics High Energy Physics - Theory

Abstract

We propose a numerical method for resummation of perturbative series, which is based on the stochastic perturbative solution of Schwinger-Dyson equations. The method stochastically estimates the coefficients of perturbative series, and incorporates Borel resummation in a natural way. Similarly to the "worm" algorithm, the method samples open Feynman diagrams, but with an arbitrary number of external legs. As a test of our numerical algorithm, we study the scale dependence of the renormalized coupling constant in a theory of one-component scalar field with quartic interaction. We confirm the triviality of this theory in four and five space-time dimensions, and the instability of the trivial fixed point in three dimensions.

Keywords

Cite

@article{arxiv.1104.3459,
  title  = {A method for resummation of perturbative series based on the stochastic solution of Schwinger-Dyson equations},
  author = {P. V. Buividovich},
  journal= {arXiv preprint arXiv:1104.3459},
  year   = {2011}
}

Comments

15 pages RevTeX, 9 figures; v2: matches published version, some clarifying remarks added, discussion of the applicability of the method to non-Abelian gauge theories extended