Noncommutative geometry in quantum field theory and the cosmogenic neutrino physics at the extreme energies

Abstract: Analysis of the covariant theta-exact noncommutative (NC) gauge field theory (GFT), inspired by high energy cosmic rays experiments, is performed in the framework of the inelastic neutrino-nucleon scatterings. Next we have have found neutrino two-point function and shows a closed form decoupled from the hard ultraviolet (UV) divergent term, from softened ultraviolet/infrared (UV/IR) mixing term, and from the finite terms as well. For a certain choice of the noncommutative parameter theta which preserves unitarity, problematic UV divergent and UV/IR mixing terms vanish. Non-perturbative modifications of the neutrino dispersion relations are assymptotically independent of the scale of noncommutativity in both, the low and high energy limits and may allow superluminal propagation.