skip to main content

SciTech ConnectSciTech Connect

Title: Generalized constructive tree weights

The Loop Vertex Expansion (LVE) is a quantum field theory (QFT) method which explicitly computes the Borel sum of Feynman perturbation series. This LVE relies in a crucial way on symmetric tree weights which define a measure on the set of spanning trees of any connected graph. In this paper we generalize this method by defining new tree weights. They depend on the choice of a partition of a set of vertices of the graph, and when the partition is non-trivial, they are no longer symmetric under permutation of vertices. Nevertheless we prove they have the required positivity property to lead to a convergent LVE; in fact we formulate this positivity property precisely for the first time. Our generalized tree weights are inspired by the Brydges-Battle-Federbush work on cluster expansions and could be particularly suited to the computation of connected functions in QFT. Several concrete examples are explicitly given.
Authors:
 [1] ;  [2]
  1. LPT, CNRS UMR 8627, Univ. Paris 11, 91405 Orsay Cedex, France and Perimeter Institute for Theoretical Physics, 31 Caroline St. N, Ontario N2L 2Y5, Waterloo (Canada)
  2. Université Paris 13, Sorbonne Paris Cité, 99, Avenue Jean-Baptiste Clément LIPN, Institut Galilée, CNRS UMR 7030, F-93430 Villetaneuse, France and Horia Hulubei National Institute for Physics and Nuclear Engineering, P.O.B. MG-6, 077125 Magurele (Romania)
Publication Date:
OSTI Identifier:
22250773
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 55; Journal Issue: 4; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; CALCULATION METHODS; CLUSTER EXPANSION; DIAGRAMS; FUNCTIONS; GRAPH THEORY; PARTITION; PERTURBATION THEORY; QUANTUM FIELD THEORY; SYMMETRY