Chen's Iterated Integral represents the Operator Product Expansion

Details Chen's Iterated Integral represents the Operator Product Expansion Chen's Iterated Integral represents the Operator Product Expansion

1999-01-21

arxiv.org/abs/hep-th/9901099v5

Adv.Theor.Math.Phys. 3 (2000) 3; Adv.Theor.Math.Phys. 3 (1999) 627-670

Physics

High Energy Physics

High Energy Physics - Theory

35p, LaTeX, using epsf for four figures. References updated and typos corrected

Scientific paper

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.

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