Exponential renormalization

Abstract

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).

revised version; accepted for publication in Annales Henri Poincare

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Cited by in corpus (13)

• Exponential Renormalization II: Bogoliubov's R-operation and momentum subtraction schemes
• From dynamical systems to renormalization
• Groupoids and Faa di Bruno formulae for Green functions in bialgebras of trees
• Some combinatorial aspects of quantum field theory
• Renormalization, Hopf algebras and Mellin transforms
• Scalar Resonances in the Non-linearly Realized Electroweak Theory
• Polynomial functors and combinatorial Dyson-Schwinger equations
• Faà di Bruno for operads and internal algebras
• The Stueckelberg Mechanism in the presence of Physical Scalar Resonances
• Renormalization Group Equation for Weakly Power Counting Renormalizable Theories
• Normal Products and Zimmermann Identities in Configuration Space BPHZ Renormalization
• Quantum Local Symmetry of the D-Dimensional Non-Linear Sigma Model: A Functional Approach
• Bialgebra of specified graphs and external structures