Lorentz non-invariance

Various ideas on how Lorentz invariance might be broken are reviewed, but the authors mainly study a model characterized by weak interactions having a special metric. Such a model seems not to fit together so well the three-standard deviations from Lorentz invariance that have been found respectively for π+-- and K+--lifetimes and the recent K0-anti K0 regeneration parameters analysis. Still the indication for a C-even Lorentz non-invariant interaction from the K0-anti K0 analysis agrees with the model. However, the most important blow to the hypothesis of Lorentz non-invariance in weak interactions comes from matching the resulting non-Lorentz invariant renormalization of the kinetic term in Dirac Lagrangian with Phillips experiment on the diurnal variation of the torsion moment of a ferromagnet. Some additional experimental tests at the weak interaction scale are proposed, the test of a model at a more distant (e.g. proton-decay) scale being left to a future phenomenology. (Auth.)