Complexified spinor fields in operator form

TL;DR

This paper explores the operator formalism of quantum field theory to analyze spinor fields, Lorentz transformations, and parity, providing insights into neutrino handedness and time symmetry without parity violation.

Contribution

It introduces a complexified operator formalism for spinor fields, including new operators for spin reflection and a detailed analysis of parity and time symmetry in quantum fields.

Findings

Spin is confirmed to be odd, with no parity violation in cobalt-60 decay.

The formalism explains the exclusive handedness of neutrinos.

Time inversion symmetry is preserved within the complexified operator framework.

Abstract

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.