Improved Epstein-Glaser renormalization in $x$-space versus differential renormalization
Abstract
Renormalization of massless Feynman amplitudes in -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.
Cite
@article{arxiv.1403.1785,
title = {Improved Epstein-Glaser renormalization in $x$-space versus differential renormalization},
author = {José M. Gracia-Bondía and Heidy Gutiérrez and Joseph C. Várilly},
journal= {arXiv preprint arXiv:1403.1785},
year = {2017}
}
Comments
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