From quantum electrodynamics to posets of planar binary trees

Frédéric Chapoton (1) , Alessandra Frabetti (1)

1 ICJ - Institut Camille Jordan

This paper is a brief mathematical excursion which starts from quantum electrodynamics and leads to the Moebius function of the Tamari lattice of planar binary trees, within the framework of groups of tree-expanded series. First we recall Brouder's expansion of the photon and the electron Green's functions on planar binary trees, before and after the renormalization. Then we recall the structure of Connes and Kreimer's Hopf algebra of renormalization in the context of planar binary trees, and of their dual group of tree-expanded series. Finally we show that the Moebius function of the Tamari posets of planar binary trees gives rise to a particular series in this group.

Mots clés: Hopf algebra; renormalization; trees; series

Domaines: Algèbres quantiques [math.QA]; Physique mathématique [math-ph]

Frédéric Chapoton, Alessandra Frabetti. From quantum electrodynamics to posets of planar binary trees. Proceedings of the Mini-workshop on Renormalization held December 15-16, 2006, and the Conference on Combinatorics and Physics held March 19-23, 2007, in Bonn, 2007, Bonn, Germany. pp.53--66. ⟨hal-00342711⟩