Neutrino Oscillations in Four-dimension Space

Quantum gravity contains incoherent microscopic models with stochastic metric. Decoherence appeared in these models have contributions from stochastic quantum Gravity, which is operating as an effective medium, as well as from conventional uncertainties in the energy of the neutrino (anti-neutrino) beam. All these contributions lead to damping factors modulating the oscillatory terms. In some theoretical models, the phenomenon of spacetime may be incorporated [1]. According to this picture, the singular microscopic fluctuations of the metric give the ground state of quantum gravity of the structure of a stochastic medium. The medium has the profound effect of CPT-violating [2] decoherence of quantum matter as it propagates. This may have experimentally observable consequences in principle [3]. One of the basic effects of gravitational de-coherence is the presence of factors which damp oscillatory terms or coherence. Space-time foam models do not consist exclusively of microscopic black holes, although there are the most popular models, another types of foam, inspired by brain-world scenarios [14]. We do not explain this subject here. The most important things here is that to discuss the neutrino oscillation. The neutrino oscillation can be studied in the stochastic quantum gravity environment [16]. Measurable quantities, such as transition amplitudes between neutrino flavors will be obtained by averaging over the stochastic variables hμν . The influence of the quantum gravity environment has a de-coherence effect on the neutrino state which is equivalent to a damping of the oscillations between neutrino flavors [13]. The determination of the particular