Francis Brown, Karen Yeats
Spanning Forest Polynomials and the Transcendental Weight of Feynman Graphs
Preprint series: ESI preprints

MSC:

81Q05 Closed and approximate solutions to the Schrodinger, Dirac, Klein-Gordon and other quantum-mechanical equations

81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis

Abstract: We give combinatorial criteria for predicting the transcendental
weight of Feynman integrals of certain graphs in $\phi^4$ theory.
By studying spanning forest polynomials, we obtain operations on
graphs which are weight-preserving, and a list of subgraphs which
induce a drop in the transcendental weight.