In a recent work a modified BPHZ scheme has been introduced and applied to one-loop Feynman graphs in non-commutative φ{symbol} 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. © 2013 Springer-Verlag Berlin Heidelberg and Società Italiana di Fisica.
CITATION STYLE
Blaschke, D. N., Gieres, F., Heindl, F., Schweda, M., & Wohlgenannt, M. (2013). BPHZ renormalization and its application to non-commutative field theory. European Physical Journal C, 73(9), 1–16. https://doi.org/10.1140/epjc/s10052-013-2566-8
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