Octonic relativistic quantum mechanics

TL;DR

This paper introduces a novel octonic framework for relativistic quantum mechanics, generalizing wave functions to eight components, describing spin-1/2 particles with specific spatial structures, and connecting to Maxwell-like and Dirac equations.

Contribution

It develops an octonic algebra-based relativistic quantum mechanics, introducing eight-component spinors and reformulating equations analogous to Maxwell and Dirac equations.

Findings

Octonic wave function describes spin-1/2 particles with specific spatial structures.

Eight-component spinors separate different spin, particle-antiparticle, and polarization states.

Second-order equations can be reformulated as Maxwell-like systems or reduced to Dirac-like equations.

Abstract

In this paper we represent the generalization of relativistic quantum mechanics on the base of eght-component values "octons", generating associative noncommutative spatial algebra. It is shown that the octonic second-order equation for the eight-component octonic wave function, obtained from the Einshtein relation for energy and momentum, describes particles with spin of 1/2. It is established that the octonic wave function of a particle in the state with defined spin projection has the specific spatial structure in the form of octonic oscillator with two spatial polarizations: longitudinal linear and transversal circular. The relations between bispinor and octonic descriptions of relativistic particles are established. We propose the eight-component spinors, which are octonic generalisation of two-component Pauli spinors and four-component Dirac bispinors. It is shown that proposed eight-component spinors separate the states with different spin projection, different particle-antiparticle state as well as different polarization of the octonic oscillator. We demonstrate that in the frames of octonic relativistic quantum mechanics the second-order equation for octonic wave function can be reformulated in the form of the system of first-order equations for quantum fields, which is analogous to the system of Maxwell equations for the electromagnetic field. It is established that for the special type of wave functions the second-order equation can be reduced to the single first-order equation, which is analogous to the Dirac equation. At the same time it is shown that this first-order equation describes particles, which do not create quantum fields.