The high energy neutrino transitions with the photon and electron-positron pair creation in a strong magnetic field in the framework of the Standard Model are investigated. The process probabilities and the mean values of the neutrino energy and momentum loss are presented. The asymmetry of outgoing neutrinos, as a possible source of sufficient recoil ``kick'' velocity of a remnant and the emission of e+ e- pairs and gamma-quanta in a ``polar cap'' region of a remnant, as a possible origin of cosmological gamma-burst are discussed.

Radiative decay of the massive neutrino ni(i) --> nu(j)gamma(m(i) > m(j)) in a constant crossed electromagnetic field is investigated within the framework of the standard electroweak theory. It is shown that the decay is catalyzed by the external field. This effect becomes significant in a strong crossed field (F much greater than B(e) = m(e)2/e congruent-to 4.41 x 10(13) G) and even more pronounced for the ultrarelativistic neutrino (E(nu) much greater than m(nu)) in a relatively weak field (F much less than B(e)).

The Weinberg-Salam model with fermion mixing is used to calculate the amplitude for the nondiagonal process f(i)gamma --> f(j)gamma with arbitrary fermions (quarks or leptons), both up and down. The only assumptions used are m(i)2, m(j)2 much less than m(w)2. It is shown that the total contribution of the counterterms to the amplitude of the process is zero. The expression obtained for the amplitude agrees with existing results in special cases.

In the framework of the Glashow-Weinberg-Salam theory in the quark approach the rare decay K(L)0 --> mu+-mu- is analyzed. Using recent experimental measurements of Br (K(L)0 --> mu+-mu-) and Br (K(L)0 --> 2-gamma), and also of the elements V(ub) and V(cb) of the Kobayashi-Maskawa matrix, the following bounds are obtained on the mass of the t quark: m(t) = 123(-35)+27 GeV.