CPTInvariance and Weak Interactions

The pure leptonic and semileptonic weak interactions, together with the possible violation of $\mathrm{CPT}$ invariance, are studied by explicitly constructing a model of weak interactions. At low energies, we have the Fermi effective Lagrangian. The divergences in the model are no worse than those in the well-known renormalizable theories. The model suggests that if $\mathrm{CPT}$ invariance is violated in the weak interactions, so is Lorentz invariance. Furthermore, $\mathrm{CPT}$ violation cannot be detected by measuring the difference of lifetime, mass, or magnetic moment between the usually observed particle and antiparticle. It should be tested by measuring the deviation of the particle lifetime at high energies. Experimentally, the lifetimes of the charged kaon and the muon appear to be shorter at higher energies, as predicted by the model. The model is in agreement with the known experiments and gives many specific predictions.