Feynman Diagrams and Rooted Maps
Nuclear Theory
2017-07-13 v3 High Energy Physics - Phenomenology
Mathematical Physics
math.MP
Quantum Physics
Abstract
The Rooted Maps Theory, a branch of the Theory of Homology, is shown to be a powerful tool for investigating the topological properties of Feynman diagrams, related to the single particle propagator in the quantum many-body systems. The numerical correspondence between the number of this class of Feynman diagrams as a function of perturbative order and the number of rooted maps as a function of the number of edges is studied. A graphical procedure to associate Feynman diagrams and rooted maps is then stated. Finally, starting from rooted maps principles, an original definition of the genus of a Feynman diagram, which totally differs from the usual one, is given.
Cite
@article{arxiv.1312.0934,
title = {Feynman Diagrams and Rooted Maps},
author = {A. Prunotto and W. M. Alberico and P. Czerski},
journal= {arXiv preprint arXiv:1312.0934},
year = {2017}
}
Comments
20 pages, 30 figures, 3 tables