On the broken gauge, conformal and discrete symmetries in particle physics

Relationships between gauge, conformal and discrete symmetries in particle physics are analysed. We study also the effect of the electroweak mixing on the cancellation of SU(2) anomalous actions. It is shown that the relation theta_{W} = 2(theta_{12}+theta_{23}+theta_{13}) between the Weinberg angle and the Cabibbo-Kobayashi-Maskawa angles should be satisfied and this effect is completely defined by the mixing of Dirac fermions. We compare two mechanisms of the spontaneous breaking of gauge symmetry, discuss the renormalizability of theories, and argue for the existence of the Majorana fermions necessary to remove the SU(2) anomalous action. The fate of the majoron and the spontaneously broken lepton number is discussed. We also show the compatibility of the boson and fermion mixings with Dyson-Schwinger equations.