Cohomological analysis of the Epstein-Glaser renormalization
نویسنده
چکیده
A cohomological analysis of the renormalization freedom is performed in the Epstein-Glaser scheme on a flat Euclidean space. We study the deviation from commutativity between the renormalization and the action of all linear partial differential operators. It defines a natural Hochschild 1–cocycle and the renormalization ambiguity exactly corresponds to the cohomological class of this renormalization cocycle. Furthermore, we have shown that the related cohomology spaces can be reduced to de Rham cohomologies of the so called “(ordered) configuration spaces”. We have also found cohomological differential equations that determine the renormalization cocycles up to the renormalization freedom. This analysis is a first step towards a new approach for computing renormalization group actions. It can be also naturally extended to manifolds as well as to the case of causal perturbation theory.
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