Improved Epstein-Glaser renormalization in $x$-space versus differential renormalization

Abstract

Renormalization of massless Feynman amplitudes in $x$-space is reexamined here, using almost exclusively real-variable methods. We compute a wealth of concrete examples by means of recursive extension of distributions. This allows us to show perturbative expansions for the four-point and two-point functions at several loop order. To deal with internal vertices, we expound and expand on convolution theory for log-homogeneous distributions. The approach has much in common with differential renormalization as given by Freedman, Johnson and Latorre; but differs in important details.

Latex, 47 pages. v2: Some reorganization, minor improvements, 4 added references. v3: Minor corrections to match published version v4: Appendix B completed (with respect to the published version) by supplying a missing contribution to the two-point function, following a suggestion of Schnetz [26]; and a few misprints corrected

References in corpus (5)

• Dimensional Regularization in Position Space, and a Forest Formula for Epstein-Glaser Renormalization
• Renormalization of Massless Feynman Amplitudes in Configuration Space
• Dimensional Regularization in Position Space and a Forest Formula for Regularized Epstein-Glaser Renormalization
• Renormalization of quantum field theory on curved space-times, a causal approach
• The scaling and mass expansion

Cited by in corpus (7)

• Quantum gravitational corrections for spinning particles
• Stora's fine notion of divergent amplitudes
• Dynamical residues of Lorentzian spectral zeta functions
• CFT in Conformally Flat Spacetimes
• Relativistic causality and position space renormalization
• Diphoton decay of the higgs from the Epstein--Glaser viewpoint
• Massless fields and adiabatic limit in quantum field theory