Kilometer3-scale neutrino detectors such as IceCube, ANTARES, and the proposed Km3Net neutrino observatory in the Mediterranean have measured, and will continue to characterize, the atmospheric neutrino spectrum above 1 TeV. Such precise measurements enable us to probe new neutrino physics, in particular, those that arise from Lorentz violation. In this paper, we first relate the effective new physics hamiltonian terms with the Lorentz violating literature. Second, we calculate the oscillation probability formulas for the two-level vμ-vτ sector. Finally, we comment on some of the challenges and outlook for this analysis.National Science Foundation (U.S.) (Grant 1505858)National Science Foundation (U.S.) (Grant 1505855)Science and Technology Facilities Council (Great Britain
