How to Resum Feynman Graphs

Understand

In this paper we reformulate in a simpler way the combinatoric core of constructive quantum field theory We define universal rational combinatoric weights for pairs made of a graph and one of its spanning trees.

• These weights are nothing but the percentage of Hepp's sectors in which the tree is leading the ultraviolet analysis.
• We explain how they allow to reshuffle the divergent series formulated in terms of Feynman graphs into convergent series indexed by the trees that these graphs contain.
• The Feynman graphs to be used are not the ordinary ones but those of the intermediate field representation, and the result of the reshuffling is called the Loop Vertex Expansion.