Generalized constructive tree weights
- 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)
- 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)
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.
- OSTI ID:
- 22250773
- Journal Information:
- Journal of Mathematical Physics, Vol. 55, Issue 4; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
- Country of Publication:
- United States
- Language:
- English
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