An Axial Vector Photon in a Mirror World

TL;DR

This paper proposes a new theoretical framework for axial-vector photons in a mirror world, involving generalized equations and gauge transformations that account for their unique properties and interactions.

Contribution

It introduces a novel approach to axial-vector photons, including generalized Klein-Gordon and Dirac equations, and a new gauge transformation responsible for their mass and neutrality.

Findings

Axial-vector photons have different lifetimes and properties based on their components.

A generalized Klein-Gordon equation is developed for C-odd particles with nonzero spin.

A new gauge transformation explains the origin of axial-vector mass in the interaction Lagrangian.

Abstract

The unity of symmetry laws emphasizes, in the case of a mirror CP-even Dirac Lagrangian, the regularity that the left- and right-handed axial-vector photons refer to long- and short-lived bosons of true neutrality, respectively. Such a difference in lifetimes expresses the unidenticality of masses, energies, and momenta of axial-vector photons of the different components. They require the generalization of the classical Klein-Gordon equation to the case of C-odd types of particles with a nonzero spin. Together with a new Dirac equation for truly neutral particles with the half-integral spin, the latter reflects the availability in nature of the second type of the local axial-vector gauge transformation responsible for origination in a Lagrangian of C-oddity of an interaction Newton component, which gives an axial-vector mass to all the interacting particles and fields. The quantum axial-vector mass, energy, and momentum operators constitute herewith the CP-invariant Schr\"odinger equation, confirming that each of them can individually influence on the matter field. Thereby, findings define at the new level, namely, at the level of the mass-charge structure of gauge invariance the mirror Euler-Lagrange equation such that it has an axial-vector nature.