R. Horvat, A. Ilakovac, J. Trampetic, J. You
We study one-loop photon and neutrino self-energies on spaces deformed by the spacetime noncommutativity, in U(1) gauge-theory in four and two dimensions. Closed form results in four-dimensions show that both self-energies contain a hard ultraviolet divergence, different power ultraviolet/infrared mixing terms, as well as a softened logarithmic infrared divergent term of the type ln(\mu^2(\theta p)^2). In two-dimensional space, all divergences from certain planar plus non-planar graphs for both the photon and neutrino two-point functions are eliminated with the unique choice of deformation freedom parameter \kappa_f=1. In this case for photon self-energy we have found solely finite planar diagram contribution: -2e^2/\pi, while the contribution to the neutrino self-energy does vanish.
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http://arxiv.org/abs/1306.1239
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