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Chen's Iterated Integral represents the Operator Product Expansion

Dirk Kreimer
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Abstract

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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Dirk Kreimer. 1999-09-18. Chen's Iterated Integral represents the Operator Product Expansion. https://arxiv.org/abs/hep-th/9901099

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