<p>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 to analyze 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 provided using the 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 Schrödinger equation and this is done by the Wick rotations of involved operators and vectors of the complexified formalism.</p>