Neutrino masses in SU(2) ⊗ U(1) theories

We analyze SU(2)×U(1) theories, denoted by ($n, m$), in which there are $n$ neutrinos belonging to isodoublets and $m$ neutrino isosinglets. The charged-current weak interactions are described by a rectangular matrix $K$ which we explicitly parametrize. The neutral-current neutrino interactions are described by a square matrix $P=K^{+}K$. This has the consequences that neutrinos may decay into three lighter ones and that neutrino oscillations involving neutral-current interactions should exist. The general formalism for the latter situation is given. Associated material on parametrization of unitary matrices and the quantum theory of Majorana particles is also briefly discussed.