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BPHZ renormalization and its application to non-commutative field theory

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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http://hal.in2p3.fr/in2p3-00872611
Contributor : Dominique Girod <>
Submitted on : Monday, October 14, 2013 - 10:20:24 AM
Last modification on : Tuesday, November 19, 2019 - 2:38:08 AM

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D.N. Blaschke, F. Gieres, F. Heindl, M. Schweda, M. Wohlgenannt. BPHZ renormalization and its application to non-commutative field theory. European Physical Journal C: Particles and Fields, Springer Verlag (Germany), 2013, 73, pp.2566. ⟨10.1140/epjc/s10052-013-2566-8⟩. ⟨in2p3-00872611⟩

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