Relativistic causality and position space renormalization

Abstract

The paper gives a historical survey of the causal position space renormalization with a special attention to the role of Raymond Stora in the development of this subject. Renormalization is reduced to subtracting the pole term in analytically regularized primitively divergent Feynman amplitudes. The identification of residues with "quantum periods" and their relation to recent developments in number theory are emphasized. We demonstrate the possibility of integration over internal vertices (that requires control over the infrared behavior) in the case of the massless ${\phi }^4$ theory and display the dilation and the conformal anomaly.

16 pages, 1 figure

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Cited by in corpus (4)

• Hepp's bound for Feynman graphs and matroids
• Stora's fine notion of divergent amplitudes
• Coordinate space representation for renormalization of quantum electrodynamics
• Hyperlogarithms and periods in Feynman amplitudes