Centre for Particle Theory Colloquia: Dyson-Schwinger solutions from the Hopf algebra of renormalization
24 February 2004 16:00 in CLC 202
"Until recently, we knew of only two types diagram allowing all-orders summation: ladders and chains. We now know that the Hopf algebra of rooted trees organizes the iterated subtraction of subdivergences generated by all nestings and chainings of primitive divergences. It thus offers the prospect of more powerful summations of renormalized perturbative quantum field theory. I shall describe the analytical, combinatoric and Hopf-algebraic structure of a summation of diagrams whose divergence structure is described by undecorated rooted trees, generated by a single skeleton term. The exact results will be compared with Pade-Borel approximations. The Hopf algebra reveals a remarkable structure that enables the momentum dependence of the sum of diagrams to be reconstructed from a non-perturbative result for an anomalous dimension. "
Coffee and biscuits at 15:30 in CM 211 (Maths Coffee Room).