Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
1999-09-24
Phys.Rev.Lett.84:2318-2321,2000
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
RevTeX, 5pp, no figures. Notation of a sum in Eq.(2) improved. Slight modifications in redaction. Final version to appear in P
Scientific paper
10.1103/PhysRevLett.84.2318
Massive spin-1/2 fields are studied in the framework of loop quantum gravity by considering a state approximating, at a length scale $\cal L$ much greater than Planck length $\ell_P=1.2\times 10^{-33}$cm, a spin-1/2 field in flat spacetime. The discrete structure of spacetime at $\ell_P$ yields corrections to the field propagation at scale $\cal L$. Next, Neutrino Bursts (${\bar p}\approx 10^5$GeV) accompaning Gamma Ray Bursts that have travelled cosmological distances, $L\approx 10^{10}$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 $({\bar p} \ell_P) L/c\approx 10^4$s. To next order in ${\bar p} \ell_P$ the correction has the form of the Gambini and Pullin effect for photons. Its contribution to time delay is comparable to that caused by the mass term. Finally, a dependence $L_{\rm os}^{-1} \propto {\bar p}^2 \ell_P$ is found for a two-flavour neutrino oscillation length.
Alfaro Jorge
Morales-Tecotl Hugo A.
Urrutia Luis F.
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