MATHEMATICAL PHYSICS SECTOR'S SEMINAR



SEMINAR ON:
"The Hopf algebra of Feynman graphs in QED"

Dott. Walter VAN SUIJLEKOM

Max Planck Institute for Mathematics


After recalling the Hopf algebraic approach to renormalization in quantum
field theory, we describe the Hopf algebra of Feynman graphs in quantum
electrodynamics.  The Ward-Takahashi identities are implemented as linear
relations on this (commutative) Hopf algebra. Compatibility of these
relations with the Hopf algebra structure is the mathematical formulation of
the physical fact that WT-identities are compatible with renormalization. As
a result, the counterterms and the renormalized Feynman amplitudes
automatically satisfy the WT-identities, which leads in particular to the
well-known identity $Z_1=Z_2$.




Thu. 6 April 2006 @ 17.00
SISSA - Main Building - room E