Self-energies on deformed spacetimes
Abstract
We study one-loop photon (Pi) and neutrino (Sigma) self-energies in a U(1) covariant gauge-theory on d-dimensional noncommutative spaces determined by a antisymmetric-constant tensor thetamu nu. For the general fermion-photon (Sf) and photon self-interaction (Sg) the closed form results reveal self-energies besetting with all kind of pathological terms: the UV divergence, the quadratic UV/IR mixing terms as well as a logarithmic IR divergent term of the type ln(mu2(theta p)2). In addition, the photon-loop produces new tensor structures satisfying transversality condition by themselves. We show that the photon self-energy in four-dimensional Euclidean spacetime can be reduced to two finite terms by imposing a specific full rank of thetamu nu and setting deformation parameters (kappaf,kappag)=(0,3). In this case the neutrino two-point function vanishes. Thus for a specific point (0,3) in the parameter-space (kappaf,kappag), a covariant theta-exact approach is able to produce a divergence-free result for one-loop quantum corrections, having also well-defined both the commutative limit as well as the pointlike limit of an extended object. While in two-dimensional space the photon self-energy is finite for arbitrary (kappaf,kappag) combinations, the neutrino self-energy still contains an superficial IR divergence.