How to Resum Feynman Graphs

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.Comment: 18 pages, 6 figures; minor revisions; improves and replaces arXiv:1006.461

High-Resolution Photoelectron Spectroscopy of Molecules

Rotationally resolved photoelectron spectra can provide significant insight into the underlying dynamics of molecular photoionization. Here, we discuss and compare results of recent theoretical studies of rotationally resolved photoelectron spectra with measurements for molecules such as HBr, OH, NO, N_2, CO, H_2O, H_2CO, and CH_3. These studies reveal the rich dynamics of quantum-state-specific studies of molecular photoionization and provide a robust description of key spectral features resulting from Cooper minima, autoionization, alignment, partial-wave mixing, and interference in related experimental studies