  We construct self/anti-self charge conjugate (Majorana-like) states for the
(1/2, 0)+(0, 1/2) representation of the Lorentz group, and their analogs for
higher spins within the quantum field theory. The problem of the basis
rotations and that of the selection of phases in the Dirac-like and
Majorana-like field operators are considered. The discrete symmetries
properties (P, C, T) are studied. The corresponding dynamical equations are
presented. In the (1/2, 0)+(0, 1/2) representation they obey the Dirac-like
equation with eight components, which has been first introduced by Markov.
Thus, the Fock space for corresponding quantum fields is doubled (as shown by
Ziino). The particular attention has been paid to the questions of chirality
and helicity (two concepts which are frequently confused in the literature) for
Dirac and Majorana states. We further review several experimental consequences
which follow from the previous works of M.Kirchbach et al. on neutrinoless
double beta decay, and G.J.Ni et al. on meson lifetimes.
