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Journal of High Energy Physics

, 2011:81 | Cite as

On UV/IR mixing in noncommutative gauge field theories

  • R. Horvat
  • A. Ilakovac
  • J. Trampetic
  • J. You
Article

Abstract

In formulating gauge field theories on noncommutative (NC) spaces it is suggested that particles carrying gauge invariant quantities should not be viewed as pointlike, but rather as extended objects whose sizes grow linearly with their momenta. This and other generic properties deriving from the nonlocal character of interactions (showing thus unambiguously their quantum-gravity origin) lead to a specific form of UV/IR mixing as well as to a pathological behavior at the quantum level when the noncommutativity parameter θ is set to be arbitrarily small. In spite of previous suggestions that in a NC gauge theory based on the θ-expanded Seiberg-Witten (SW) maps UV/IR mixing effects may be under control, a fairly recent study of photon self-energy within a SW θ-exact approach has shown that UV/IR mixing is still present. We study the self-energy contribution for neutral massless fermions in the θ-exact approach of NC QED, and show by explicit calculation that all but one divergence can be eliminated for a generic choice of the noncommutativity parameter θ. The remaining divergence is linked to the pointlike limit of an extended object.

Keywords

Non-Commutative Geometry Nonperturbative Effects Space-Time Symmetries 

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Copyright information

© SISSA, Trieste, Italy 2011

Authors and Affiliations

  1. 1.Institute Ruder BoškovićZagrebCroatia
  2. 2.Faculty of ScienceUniversity of ZagrebZagrebCroatia
  3. 3.Max-Planck-Institut für Physik, (Werner-Heisenberg-Institut)MünchenGermany

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