The General O(n) Quartic Matrix Model and its application to Counting Tangles and Links

Paul Zinn-Justin 1

Communications in Mathematical Physics 238 (2003) 287-304

The counting of alternating tangles in terms of their crossing number, number of external legs and connected components is presented here in a unified framework using quantum field-theoretic methods applied to a matrix model of colored links. The overcounting related to topological equivalence of diagrams is removed by means of a renormalization scheme of the matrix model; the corresponding « renormalization equations » are derived. Some particular cases are studied in detail and solved exactly.

  • 1. Laboratoire de Physique Théorique et Hautes Energies (LPTHE),
    CNRS : UMR7589 – Université Paris VI – Pierre et Marie Curie – Université Paris VII – Paris Diderot
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