Quantum gravity corrections to neutrino propagation

Massive spin-1/2 fields are studied in the framework of loop quantum gravity by considering a state approximating, at a length scale L much greater than Planck length l(P), a spin-1/2 field in flat spacetime. The discrete structure of spacetime at l(P) yields corrections to the field propagation at scale L. Neutrino bursts ( &pmacr; approximately 10(5) GeV) accompanying gamma ray bursts that have traveled cosmological distances L are considered. The dominant correction is helicity independent and leads to a time delay of order (&pmacr;l(P))L/c approximately 10(4) s. To next order in &pmacr;l(P), the correction has the form of the Gambini and Pullin effect for photons. A dependence L(-1)(os) approximately &pmacr;(2)l(P) is found for a two-flavor neutrino oscillation length.