Chen’s iterated integral represents the operator product expansion

Chen's Iterated Integral represents the Operator Product Expansion

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 ide...

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ar X iv : h ep - t h / 99 01 09 9 v 2 2 2 Ja n 19 99 Chen ’ s Iterated Integral represents the Operator Product Expansion

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 i...

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/ 99 01 09 9 v 1 2 1 Ja n 19 99 Chen ’ s Iterated Integral represents the Operator Product Expansion

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 i...

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Operator product expansion and analyticity

We discuss the current use of the operator-product expansion in QCD calculations. Treating the OPE as an expansion in inverse powers of an energy-squared variable (with possible exponential terms added), approximating the vacuum expectation value of the operator product by several terms and assuming a bound on the remainder along the euclidean region, we observe how the bound varies with increa...

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Operator product expansion and confinement

Operator product expansion technique is analyzed in abelian and nonabelian field theoretical models with confinement. Special attention is paid to the regimes where nonzero virtuality of vacuum fields is felt by external currents. It is stressed that despite the physics of confinement is sometimes considered as being caused by " soft " fields, it can exhibit the pronounced " hard " effects in OPE.

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Chen’s iterated integral represents the operator product expansion

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