of neutrino oscillations was tested, which could arise when there were a preferred background field. This, possible CPT violations, and other coefficients of Lorentz violations in the framework of SME, have been tested. Here, some of the achieved GeV bounds for the validity of Lorentz invariance are stated: Neutrino speed Since the discovery of neutrino oscillations, it is assumed that their speed is slightly below the speed of light. Direct velocity measurements indicated an upper limit for relative speed differences between light and neutrinos of , see measurements of neutrino speed. Also indirect constraints on neutrino velocity, on the basis of effective field theories such as SME, can be achieved by searching for threshold effects such as Vacuum Cherenkov radiation. For example, neutrinos should exhibit Bremsstrahlung in the form of electron-positron pair production. Another possibility in the same framework is the investigation of the decay of pions into muons and neutrinos. Superluminal neutrinos would considerably delay those decay processes. The absence of those effects indicate tight limits for velocity differences between light and neutrinos. Velocity differences between neutrino flavors can be constrained as well. A comparison between muon- and electron-neutrinos by Coleman & Glashow (1998) gave a negative result, with bounds <6. Reports of alleged Lorentz violations Open reports LSND, MiniBooNE In 2001, the LSND experiment observed a 3.8σ excess of antineutrino interactions in neutrino oscillations, which contradicts the standard model. First results of the more recent MiniBooNE experiment appeared to exclude this data above an energy scale of 450 MeV, but they had checked neutrino interactions, not antineutrino ones. In 2008, however, they reported an excess of electron-like neutrino events between 200 and 475 MeV. And in 2010, when carried out with antineutrinos (as in LSND), the result was in agreement with the LSND result, that is, an excess at the energy scale from 450 to 1250 MeV was observed. Whether those anomalies can be explained by sterile neutrinos, or whether they indicate Lorentz violations, is still discussed and subject to further theoretical and experimental researches. Solved reports In 2011 the OPERA Collaboration published (in a non-peer reviewed arXiv preprint) the results of neutrino measurements, according to which neutrinos were traveling slightly faster than light. The neutrinos apparently arrived early by ~60 ns. The standard deviation was 6σ, clearly beyond the 5σ limit necessary for a significant result. However, in 2012 it was found that this result was due