Lorentz violation (LV) is predicted by some quantum gravity theories, where photon dispersion relation is modified, and the speed of light becomes energydependent. Consequently, it results in a tiny time delay between high energy photons and low energy ones. Very high energy (VHE) photon emissions from cosmological distance can amplify these tiny LV effects into observable quantities. Here we analyze four VHE γ-ray bursts (GRBs) from Fermi observations, and briefly review the constraints from three TeV flares of active galactic nuclei (AGNs) as well. One step further, we present a first robust analysis of VHE GRBs taking the intrinsic time lag caused by sources into account, and give an estimate to quantum gravity energy ∼ 2 × 10 17 GeV for linear energy dependence, and ∼ 5 × 10 9 GeV for quadratic dependence. However, the statistics is not sufficient due to the lack of data, and further observational results are desired to constrain LV effects better.

We obtain modified dispersion relations by requiring the vanishing of determinant of inverse of modified photon propagators in Lorentz invariance violation (LIV) theory. Inspired by these dispersion relations, we give a more general dispersion relation with less assumption and apply it to the recent observed gamma-ray burst GRB090510 to extract various constraints on LIV parameters. We find that the constraint on quantum gravity mass is slightly larger than the Planck mass but is consistent with other recent observations, so the corresponding LIV coefficient ξ1 has reached the natural order (O(1)) as one expects. From our analysis, the linear LIV corrections to photon group velocity might be not excluded yet.

We derive a modified dispersion relation (MDR) in the Lorentz violation extension of quantum electrodynamics (QED) sector in the standard model extension (SME) framework. Based on the extended Dirac equation and corresponding MDR, we observe the resemblance of the Lorentz violation coupling with spin-gravity coupling. We also develop a neutrino oscillation mechanism induced by the presence of nondiagonal terms of Lorentz violation couplings in 2-flavor space in a 2-spinor formalism by explicitly assuming neutrinos to be Marjorana fermions. We also obtain a much stringent bound (∽ 10 −25 ) on one of the Lorentz violation parameters by applying MDR to the ultrahigh energy cosmic ray (UHECR) problem.

In close analogy with optical Fabry-Pérot (FP) interferometer, we rederive the transmission and reflection coefficients of tunneling through a rectangular double barrier (RDB). Based on the same analogy, we also get an analytic finesse formula for its filtering capability of matter waves, and with this formula, we reproduce the RDB transmission rate in exactly the same form as that of FP interferometer. Compared with the numerical results obtained from the original finesse definition, we find the formula works well. Next, we turn to the elusive time issue in tunneling, and show that the "generalized Hartman effect" can be regarded as an artifact of the opaque limit βl → ∞. In the thin barrier approximation, phase (or dwell) time does depend on the free inter-barrier distance d asymptotically. Further, the analysis of transmission rate in the neighborhood of resonance shows that, phase (or dwell) time could be a good estimate of the resonance lifetime. The numerical results from the uncertainty principle support this statement. This fact can be viewed as a support to the idea that, phase (or dwell) time is a measure of lifetime of energy stored beneath the barrier. To confirm this result, we shrink RDB to a double Dirac δ-barrier. The landscape of the phase (or dwell) time in k and d axes fits excellently well with the lifetime estimates near the resonance. As a supplementary check, we also apply phase (or dwell) time formula to the rectangular well, where no obstacle exists to the propagation of particle. However, due to the self-interference induced by the common cavity-like structure, phase (or dwell) time calculation leads to a counterintuitive "slowing down" effect, which can be explained appropriately by the lifetime assumptions.

General spacetime nonmetricity coupled to neutrons is studied. In this context, it is shown that certain nonmetricity components can generate a rotation of the neutron's spin. Available data on this effect obtained from slow-neutron propagation in liquid helium are used to constrain isotropic nonmetricity components at the level of 10 −22 GeV. These results represent the first limit on the nonmetricity ζ (6) 2 S 000 parameter as well as the first measurement of nonmetricity inside matter.