Euclidean Configuration Space Renormalization, Residues and Dilation Anomaly1

Nikolay M. Nikolov (1) , Raymond Stora (2, 3) , Ivan Todorov (4, 5)

1 Institute for Nuclear Research and Nuclear Energy
2 CERN - European Organization for Nuclear Research
3 LAPTH - Laboratoire d'Annecy-le-Vieux de Physique Théorique
4 CERN TH - European Organization for Nuclear Research TH
5 IHES - Institut des Hautes Études Scientifiques

Configuration (x-)space renormalization of euclidean Feynman amplitudes in a massless quantum field theory is reduced to the study of local extensions of associate homogeneous distributions. Primitively divergent graphs are renormalized, in particular, by subtracting the residue of an analytically regularized expression. Examples are given of computing residues that involve zeta values. The renormalized Green functions are again associate homogeneous distributions of the same degree that transform under indecomposable representations of the dilation group.

Domaines: Physique des Hautes Energies - Théorie [hep-th]

Nikolay M. Nikolov, Raymond Stora, Ivan Todorov. Euclidean Configuration Space Renormalization, Residues and Dilation Anomaly1. 2012. ⟨hal-00703709⟩