BPHZ renormalization and its application to non-commutative field theory
High Energy Physics - Theory
2013-09-25 v2
Abstract
In a recent work a modified BPHZ scheme has been introduced and applied to one-loop Feynman graphs in non-commutative phi^4-theory. In the present paper, we first review the BPHZ method and then we apply the modified BPHZ scheme as well as Zimmermann's forest formula to the sunrise graph, i.e. a typical higher-loop graph involving overlapping divergences. Furthermore, we show that the application of the modified BPHZ scheme to the IR-singularities appearing in non-planar graphs (UV/IR mixing problem) leads to the introduction of a 1/p^2 term and thereby to a renormalizable model. Finally, we address the application of this approach to gauge field theories.
Cite
@article{arxiv.1307.4650,
title = {BPHZ renormalization and its application to non-commutative field theory},
author = {Daniel N. Blaschke and Francois Gieres and Franz Heindl and Manfred Schweda and Michael Wohlgenannt},
journal= {arXiv preprint arXiv:1307.4650},
year = {2013}
}
Comments
27 pages, 4 figures; v2 references added, to appear in EPJC