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 P = 1.2 × 10 −33 cm, a spin-1/2 field in flat spacetime. The discrete structure of spacetime at P yields corrections to the field propagation at scale L. Next, Neutrino Bursts (p ≈ 10 5 GeV) accompaning Gamma Ray Bursts that have travelled cosmological distances, L ≈ 10 10 l.y., are considered. The dominant correction is helicity independent and leads to a time delay w.r.t. the speed of light, c, of order (p P )L/c ≈ 10 4 s. The fact that some Gamma Ray Bursts (GRB) originate at cosmological distances, (≈ 10 10 light years) [1], together with time resolutions down to submillisecond scale achieved in recent GRB data [2], suggest that it is possible to probe fundamental laws of physics at energy scales near to Planck energy E P = 1.2×10 19 GeV [3,4]. Furthermore, sensitivity will be improved with HEGRA and Whipple air Cerenkov telescopes and by AMS and GLAST spatial experiments. Thus, quantum gravity effects could be at the edge of observability [3,4]. Now, quantum gravity theories imply different spacetime structures [4,5] and it can be expected that what we consider flat spacetime, can actually involve dispersive effects arising from Planck scale lengths. Such tiny effects might become observable upon accumulation over travels through cosmological distances by energetically enough particles like cosmological GRB photons. Now, the most widely accepted model of GRB, so called fireball model, predicts also the generation of 10 14 − 10 19 eV Neutrino Bursts (NB) [7,8]. Yet, another GRB model based on cosmic strings requires neutrino production [9]. Present experiments to observe high energy astrophysical neutrinos like AMANDA, NESTOR, Baikal, ANTARES and Superkamiokande, for example, will detect at best only one or two neutrinos in coincidence with GRB's per year. The planned Neutrino Burster Experiment (NuBE) will measure the flux of ultra high energy neutrinos (> 10 TeV) over a ∼ 1km 2 effective area, in coincidence with satellite measured GRB's [10]. It is expected to detect ≈ 20 events per year, according to the fireball model. Hence, one can study quantum gravity effects on astrophysical neutrinos that might be observed or, the other way around, such observations could be used to restrict quantum gravity theories.In this letter, the loop quantum gravity framework is adopted. In this context, Gambini an Pullin studied light propagation semiclassically [6]. They found, besides departures from perfect non-dispersiveness of ordinary vacuum, helicity depending corrections for propagating waves. In the present work, the case of massive spin-1/2 particles in loop quantum gravity is studied also semiclassically. They could be identified with the neutrinos that would be produced in GRB. Central ideas and results are presented whereas details will appear elsewhere [11].Loop quantum gravity [5] uses a spin networks basis, labelled by graphs embedded in a thr...

Within loop quantum gravity we construct a coarse-grained approximation for the Einstein-Maxwell theory that yields effective Maxwell equations in flat spacetime comprising Planck scale corrections.

A simple model is constructed which allows to compute modified dispersion relations with effects from loop quantum gravity. Different quantization choices can be realized and their effects on the order of corrections studied explicitly. A comparison with more involved semiclassical techniques shows that there is agreement even at a quantitative level. Furthermore, by contrasting Hamiltonian and Lagrangian descriptions we show that possibleLorentz symmetry violations may be blurred as an artifact of the approximation scheme. Whether this is the case in a purely Hamiltonian analysis can be resolved by an improvement in the effective semiclassical analysis.

When quantum back-reaction by fluctuations, correlations and higher moments of a state becomes strong, semiclassical quantum mechanics resembles a dynamical system with a high-dimensional phase space. Here, systematic computational methods to derive the dynamical equations including all quantum corrections to high order in the moments are introduced, together with a (deparameterized) quantum cosmological example to illustrate some implications. The results show, for instance, that the Gaussian form of an initial state is maintained only briefly, but that the evolving state settles down to a new characteristic shape afterwards. Remarkably, even in the regime of large high-order moments, we observe a strong convergence within all considered orders that supports the use of this effective approach.