Mathematics – Quantum Algebra
Scientific paper
2012-02-16
Mathematics
Quantum Algebra
70 pages
Scientific paper
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.
No associations
LandOfFree
Hopf algebraic Renormalization of Kreimer's toy model does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Hopf algebraic Renormalization of Kreimer's toy model, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Hopf algebraic Renormalization of Kreimer's toy model will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-125290