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Pré-Publication, Document De Travail Année : 2013

Generalized constructive tree weights

Résumé

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.

Dates et versions

hal-00912662 , version 1 (02-12-2013)

Identifiants

Citer

Vincent Rivasseau, Adrian Tanasa. Generalized constructive tree weights. 2013. ⟨hal-00912662⟩
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