Renormalization of QED with planar binary trees

Abstract

The renormalized photon and electron propagators are expanded over planar binary trees. Explicit recurrence solutions are given for the terms of these expansions. In the case of massless Quantum Electrodynamics (QED), the relation between renormalized and bare expansions is given in terms of a Hopf algebra structure. For massive quenched QED, the relation between renormalized and bare expansions is given explicitly.

Uses feynmf package. 20 pages

References in corpus (6)

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Cited by in corpus (18)

• The Hopf algebra of Feynman graphs in QED
• Hopf Algebras in General and in Combinatorial Physics: a practical introduction
• The structure of renormalization Hopf algebras for gauge theories I: Representing Feynman graphs on BV-algebras
• Noncommutative renormalization for massless QED
• The global quantum duality principle: theory, examples, and applications
• Commutative Hopf algebras of permutations and trees
• Quantum field theory meets Hopf algebra
• Combinatorial Hopf algebras from renormalization
• Some Hopf Algebras of Trees
• The Crystal Duality Principle: from Hopf Algebras to Geometrical Symmetries
• Poisson geometrical symmetries associated to non-commutative formal diffeomorphisms
• QED Hopf algebras on planar binary trees
• Butcher series and control theory
• Loop of formal diffeomorphisms and F{à}a di Bruno coloop bialgebra
• Commutative combinatorial Hopf algebras
• A mathematical perspective on the phenomenology of non-perturbative Quantum Field Theory
• Perturbative classical and quantum field theory
• Groups of tree-expanded series