Chord diagrams and BPHZ subtractions

Abstract

The combinatorics of the BPHZ subtraction scheme for a class of ladder graphs for the three point vertex in ${\varphi }^3$ theory is transcribed into certain connectivity relations for marked chord diagrams (knots with transversal intersections). The resolution of the singular crossings using the equivalence relations in these examples provides confirmation of a proposed fundamental relationship between knot theory and renormalization in perturbative quantum field theory.

12 pages, 5 Postscript figures, LaTex 2e

References in corpus (4)

• Unknotting the polarized vacuum of quenched QED
• Habilitationsschrift: Renormalization and Knot Theory
• Knots and Divergences
• Feynman Diagram Calculations - From finite Integral Representations to knotted Infinities

Cited by in corpus (1)

• Feynman diagrams as a weight system: four-loop test of a four-term relation