Exponential renormalization

Details Exponential renormalization Exponential renormalization

2010-03-08

arxiv.org/abs/1003.1679v2

Annales Henri Poincare 11:943-971,2010

Physics

Mathematical Physics

revised version; accepted for publication in Annales Henri Poincare

Scientific paper

10.1007/s00023-010-0050-7

Moving beyond the classical additive and multiplicative approaches, we present an "exponential" method for perturbative renormalization. Using Dyson's identity for Green's functions as well as the link between the Faa di Bruno Hopf algebra and the Hopf algebras of Feynman graphs, its relation to the composition of formal power series is analyzed. Eventually, we argue that the new method has several attractive features and encompasses the BPHZ method. The latter can be seen as a special case of the new procedure for renormalization scheme maps with the Rota-Baxter property. To our best knowledge, although very natural from group-theoretical and physical points of view, several ideas introduced in the present paper seem to be new (besides the exponential method, let us mention the notions of counterfactors and of order n bare coupling constants).

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