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Renormalization theory

Renormalization is at the heart of the successful application of quantum field theory to particle physics and phase transitions in statistical mechanics. This theory has been algebraized by Connes and Kreimer, giving tools to disentangle its combinatoric and analytical aspects.

We have obtained solution to high orders of Schwinger—Dyson equations, giving new insights in quantum field theory. The objective for the next period is to get rid of the limitation to theories with divergences limited to two point functions and deal with QED and QCD. Such progress can have applications in the development of better computations for comparison with experimental data, be it for anomalous magnetic moment or strong interactions at the LHC.

We are one of the teams of the GDR renormalisation, géometrie et combinatoire.