Diagrams, Knots and Numbers

I am quite fascinated by the connection between Feynman diagrams, (positive) knots and Euler/Zagier sums.
The idea is to relate the overall counterterms of Feynman diagrams to the topology of the diagrams. This can be done by relating Feynman diagrams to positive knots. These knots match the transcendentals found in calculating these overall counterterms, as an empirical fact.
Slowly, an explanation is emerging, as there are relations to (quasi-)Hopf algebras, finite type invariants and the like, but a lot still has to be done.
A recent result along this line is that one can find Zimmermann's celebrated forest formula as an antipode in a Hopf algebra. A symbolic algebra package exemplifying this is the renormalization engine in hep-th/9810087.

For an overview of the older results, see the bibliographical notes
on papers concerning Knot/Number/Field Theory
by Broadhurst, myself, and coworkers.

For more recent work,look at my publications here.

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