Search for Lorentz Violation in km$^3$-Scale Neutrino Telescopes
  Kilometer$^3$-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 $\nu_\mu-\nu_\tau$ sector. Finally, we comment on some of the challenges and outlook for this analysis. 
C.A. Arg\"uelles, G.H. Collin, J.M. Conrad, T. Katori, A. Kheirandish
hep-ph