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Chen’s iterated integral represents the operator product expansion. (English) Zbl 0971.81093
Summary: 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.

MSC:
81T16 Nonperturbative methods of renormalization applied to problems in quantum field theory
16W30 Hopf algebras (associative rings and algebras) (MSC2000)
58D30 Applications of manifolds of mappings to the sciences
05A10 Factorials, binomial coefficients, combinatorial functions
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