Feynman diagrams and rooted maps

Feynman diagrams and rooted maps AbstractThe 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Open Physics de Gruyter

Feynman diagrams and rooted maps

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Publisher
De Gruyter
Copyright
© 2018 A. Prunotto et al., published by De Gruyter
ISSN
2391-5471
eISSN
2391-5471
D.O.I.
10.1515/phys-2018-0023
Publisher site
See Article on Publisher Site

Abstract

AbstractThe 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.

Journal

Open Physicsde Gruyter

Published: Apr 18, 2018

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