The shuffle Hopf algebra and quasiplanar Wick products

Abstract

The operator valued distributions which arise in quantum field theory on the noncommutative Minkowski space can be symbolized by a generalization of chord diagrams, the dotted chord diagrams. In this framework, the combinatorial aspects of quasiplanar Wick products are understood in terms of the shuffle Hopf algebra of dotted chord diagrams, leading to an algebraic characterization of quasiplanar Wick products as a convolution. Moreover, it is shown that the distributions do not provide a weight system for universal knot invariants.Comment: 16 pages, prepared for the conference proceedings "Non commutative Geometry and Physics", Laboratoire de physique th\'eorique d'Orsay, April 23-27, 200