Bialgebra of specified graphs and external structures
Quantum Algebra
2014-07-16 v2
Abstract
We construct a Hopf algebra structure on the space of specified Feynman graphs of a quantum field theory. We introduce a convolution product and a semigroup of characters of this Hopf algebra with values in some suitable commutative algebra taking momenta into account. We then implement the renormalization described by A. Connes and D. Kreimer and the Birkhoff decomposition for two renormalization schemes: the minimal subtraction scheme and the Taylor expansion scheme.
Cite
@article{arxiv.1306.4197,
title = {Bialgebra of specified graphs and external structures},
author = {Dominique Manchon and Mohamed Belhaj Mohamed},
journal= {arXiv preprint arXiv:1306.4197},
year = {2014}
}
Comments
21 pages. This version to appear in Annales Henri Poincar\'e S\'erie D