1999/01/31 by Dirk Kreimer · 3 citations
Physics and Astronomy · Mathematics · #hep-th #math-ph #math.MP #math.QA
published as Adv.Theor.Math.Phys. 3 (2000) 3; Adv.Theor.Math.Phys. 3 (1999) 627-670 · 35p, LaTeX, using epsf for four figures. References updated and typos corrected
arxiv created 1999/09/18 · arxiv updated 2009/11/30
The recently discovered formalism underlying renormalization theory, the Hopf algebra of rooted trees, allows to generalize Chen's lemma. In its generalized form it describes the change of a scale in Green functions, and hence relates to the operator product expansion. Hand in hand with this generalization goes the generalization of the ordinary factorial n! to the tree factorial t^!. Various identities on tree-factorials are derived which clarify the relation between Connes-Moscovici weights and Quantum Field Theory.