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The European Physical Journal C

, 73:2566 | Cite as

BPHZ renormalization and its application to non-commutative field theory

  • Daniel N. BlaschkeEmail author
  • François Gieres
  • Franz Heindl
  • Manfred Schweda
  • Michael Wohlgenannt
Regular Article - Theoretical Physics

Abstract

In a recent work a modified BPHZ scheme has been introduced and applied to one-loop Feynman graphs in non-commutative ϕ 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.

Keywords

Star Product External Momentum Feynman Integral Local Counterterm Subtraction Operator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

D.N. Blaschke is a recipient of an APART fellowship of the Austrian Academy of Sciences, and is also grateful for the hospitality of the theory division of LANL and its partial financial support. F. Gieres wishes the express his gratitude to S. Theisen for valuable discussions. M. Schweda thanks C. Becchi for useful comments.

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Copyright information

© Springer-Verlag Berlin Heidelberg and Società Italiana di Fisica 2013

Authors and Affiliations

  • Daniel N. Blaschke
    • 1
    Email author
  • François Gieres
    • 2
  • Franz Heindl
    • 3
  • Manfred Schweda
    • 3
  • Michael Wohlgenannt
    • 4
  1. 1.Theory DivisionLos Alamos National LaboratoryLos AlamosUSA
  2. 2.Institut de Physique NucléaireUniversité de Lyon, Université Lyon 1 and CNRS/IN2P3VilleurbanneFrance
  3. 3.Institute for Theoretical PhysicsVienna University of TechnologyViennaAustria
  4. 4.Austro-Ukrainian Institute for Science and Technologyc/o TU ViennaViennaAustria

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