1202.3552 (Erik Panzer)

Hopf algebraic Renormalization of Kreimer's toy model    [PDF]

Erik Panzer

This masters thesis reviews the algebraic formulation of renormalization
using Hopf algebras as pioneered by Dirk Kreimer and applies it to a toy model
of quantum field theory given through iterated insertions of a single primitive
divergence into itself. Using this example in a subtraction scheme, we exhibit
the renormalized Feynman rules to yield Hopf algebra morphisms into the Hopf
algebra of polynomials and as a consequence study the emergence of the
renormalization group in connection with combinatorial Dyson-Schwinger
equations. In particular we relate the perturbative expansion of the anomalous
dimension to the coefficients of the Mellin transform of the integral kernel
specifying the primitve divergence. A theorem on the Hopf algebra of rooted
trees relates different Mellin transforms by automorphisms of this Hopf
algebra.

View original: http://arxiv.org/abs/1202.3552