  The formalism of quantum field theory in operator form, based on the anti
self-adjoint operators of the imaginary coordinate and momentum and the
self-adjoint operators of the real coordinate, momentum, energy and time, is
used in considerations of the spinor fields and related topics. The unitary
representation of the Lorentz boosts in the spin-orbital space is given. The
operators that mirror-reflect the spin are introduced and then used in
discussion of the spin parity. The conclusion that the spin is odd is used in
the analyze of the parity violation in the cobalt-60 beta decay and it is found
that the parity is not broken. The explanation why there are only right-handed
antineutrinos and left-handed neutrinos is offered on the basis of appropriate
treatment of the influence of spin on momentum. The inversion of time is
treated within the framework of the operators of time and energy and this
symmetry is represented in a way that respects the Schr\"odinger equation and
this is done by the Wick rotations of involved operators and vectors of the
complexified formalism.
