科研之友
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摘要
In this paper, we reformulate the combinatorial core of constructive quantum field theory. We define universal rational combinatorial weights for pairs made of a graph and any of its spanning trees. These weights are simply the percentage of Hepp%26apos;s sectors of the graph in which the tree is leading, in the sense of Kruskal%26apos;s greedy algorithm. Our main new mathematical result is an integral representation of these weights in terms of the positive matrix appearing in the symmetric %26quot;BKAR%26quot; Taylor forest formula. Then, we explain how the new constructive technique called Loop Vertex Expansion reshuffles according to these weights the divergent series of the intermediate field representation into a convergent series which is the Borel sum of the ordinary perturbative Feynman%26apos;s series.
- 出版日期2014-11
