Connes-Kreimer-Epstein-Glaser Renormalization

Abstract

Causal perturbative renormalization within the recursive Epstein-Glaser scheme involves extending, at each order, time-ordered operator-valued distributions to coinciding points. This is achieved by a generalized Taylor subtraction on test functions, which is transposed to distributions. We show how the Epstein-Glaser recursive construction can, by means of a slight modification of the Hopf algebra of Feynman graphs, be recast in terms of the new Connes-Kreimer algebraic setup for renormalization. This is illustrated for ${\varphi }_4^4$-theory.

LaTeX, 34 pages, 8 included figures, Fig.5 has been changed, some improvements and one added reference

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• The uses of Connes and Kreimer's algebraic formulation of renormalization theory
• Improved Epstein-Glaser renormalization in coordinate space I. Euclidean framework
• Correlators, Feynman diagrams, and quantum no-hair in deSitter spacetime
• Species-theoretic foundations of perturbative quantum field theory