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arXiv · 1307.4650

BPHZ renormalization and its application to non-commutative field theory

Daniel N. Blaschke·Francois Gieres·Franz Heindl·Manfred Schweda·Michael Wohlgenannt
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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.

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Daniel N. Blaschke, Francois Gieres, Franz Heindl, Manfred Schweda, Michael Wohlgenannt. 2013-09-03. BPHZ renormalization and its application to non-commutative field theory. https://doi.org/10.1140/epjc%2Fs10052-013-2566-8

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