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In the standard model of neutrino oscillations, the neutrino flavor statesare mixtures of mass-eigenstates, and the phenomena are well described by theneutrino mixing matrix, i.e., the PMNS matrix. I review the recent progress onparametrization of the neutrino mixing matrix. Besides that I also discuss onthe possibility to describe the neutrino oscillations by a non-standard modelin which the neutrino mixing is caused by the Lorentz violation (LV)contribution in the effective field theory for LV. We assume that neutrinos aremassless and that neutrino flavor states are mixing states of energyeigenstates. In our calculation the neutrino mixing parts depend on LVparameters and neutrino energy. The oscillation amplitude varies with theneutrino energy, thus neutrino experiments with energy dependence may test andconstrain the Lorentz violation scenario for neutrino oscillation.

Neutrino Oscillations: from Standard and Non-standard Viewpoints