  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.
