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On the renormalization of non-commutative field theories

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

Abstract

This paper addresses three topics concerning the quantization of non-commutative field theories (as defined in terms of the Moyal star product involving a constant tensor describing the non-commutativity of coordinates in Euclidean space). To start with, we discuss the Quantum Action Principle and provide evidence for its validity for non-commutative quantum field theories by showing that the equation of motion considered as insertion in the generating functional Z c [j] of connected Green functions makes sense (at least at one-loop level). Second, we consider the generalization of the BPHZ renormalization scheme to non-commutative field theories and apply it to the case of a self-interacting real scalar field: Explicit computations are performed at one-loop order and the generalization to higher loops is commented upon. Finally, we discuss the renormalizability of various models for a self-interacting complex scalar field by using the approach of algebraic renormalization.

Keywords

Star Product External Momentum Subtraction Scheme Scalar Field Theory Wick Contraction 
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

The authors would like to express their gratitude to H. Grosse, O. Piguet and F. Vignes-Tourneret for valuable discussions.

D.N. Blaschke is a recipient of an APART fellowship of the Austrian Academy of Sciences.

We wish to thank the anonymous referees for their pertinent and constructive comments which contributed to the clarification of several points, as well as for pointing out several relevant references.

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Copyright information

© Springer-Verlag Berlin Heidelberg and Società Italiana di Fisica 2012

Authors and Affiliations

  • Daniel N. Blaschke
    • 1
    Email author
  • Thomas Garschall
    • 2
  • François Gieres
    • 3
  • Franz Heindl
    • 2
  • Manfred Schweda
    • 2
  • Michael Wohlgenannt
    • 1
    • 4
  1. 1.Faculty of PhysicsUniversity of ViennaViennaAustria
  2. 2.Institute for Theoretical PhysicsVienna University of TechnologyViennaAustria
  3. 3.Institut de Physique Nucléaire, Bat. P. DiracUniversité de Lyon, Université Lyon 1 and CNRS/IN2P3VilleurbanneFrance
  4. 4.Austro-Ukrainian Institute for Science and Technologyc/o TU ViennaViennaAustria

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