mSME coefficients lead to mixing between neutrinos and antineutrinos. These processes violate lepton-number conservation, but can readily be accommodated in the Lorentz-breaking SME framework. The breaking of invariance under rotations leads to the non-conservation of angular momentum, which allows a spin flip of the propagating neutrino that can oscillate into an antineutrino. Because of the loss of rotational symmetry, coefficients responsible for this type of mixing always introduce direction dependence. Classic CPT tests Since CPT violation implies Lorentz violation, traditional tests of CPT symmetry can also be used to search for deviations from Lorentz invariance. This test seeks evidence of . Some subtle features arise. For example, although CPT invariance implies , this relation can be satisfied even in the presence of CPT violation. Global models of neutrino oscillations with Lorentz violation Global models are descriptions of neutrino oscillations that are consistent with all the established experimental data: solar, reactor, accelerator, and atmospheric neutrinos. The general SME theory of Lorentz-violating neutrinos has shown to be very successful as an alternative description of all observed neutrino data. These global models are based on the SME and exhibit some of the key signals of Lorentz violation described in the previous section. Bicycle model The first phenomenological model using Lorentz-violating neutrinos was proposed by Kostelecky and Mewes in a 2004 paper. This so-called bicycle model exhibits direction dependence and only two parameters (two non-zero SME coefficients), instead of the six of the conventional massive model. One of the main characteristics of this model is that neutrinos are assumed to be massless. This simple model is compatible with solar, atmospheric, and long-baseline neutrino oscillation data. A novel feature of the bicycle model occurs at high energies, where the two SME coefficients combine to create a direction-dependent pseudomass. This leads to maximal mixing and an oscillation phase proportional to L/E, as in the massive case. Generalized bicycle model The bicycle model is an example of a very simple and realistic model that can accommodate most of the observed data using massless neutrinos in the presence of Lorentz violation. In 2007, Barger, Marfatia, and Whisnant constructed a more general version of this model by including more parameters. In this paper, it is shown that a combined analysis of solar, reactor, and long-baseline experiments excluded the bicycle model and its generalization. Despite this, the bicycle served as starting point for more elaborate models. Tandem model The tandem