Sedeonic relativistic quantum mechanics

TL;DR

This paper introduces sedeonic algebra to extend relativistic quantum mechanics, resulting in new equations that describe particles with spin 1/2 and potentially different neutrino types, highlighting novel algebraic and physical insights.

Contribution

It develops a sedeonic algebra framework for relativistic quantum mechanics, deriving new second- and first-order equations that generalize Dirac's theory and describe various particle types.

Findings

Sedeonic second-order equation describes spin 1/2 particles.

Reduction to sedeonic first-order equations analogous to Dirac's.

Proposed four equations for different neutrino types.

Abstract

We represent sixteen-component values "sedeons", generating associative noncommutative space-time algebra. We demonstrate a generalization of relativistic quantum mechanics using sedeonic wave functions and sedeonic space-time operators. It is shown that the sedeonic second-order equation for the sedeonic wave function, obtained from the Einstein relation for energy and momentum, describes particles with spin 1/2. We show that for the special types of wave functions the sedeonic second-order equation can be reduced to the set of sedeonic first-order equations analogous to the Dirac equation. At the same time it is shown that these sedeonic equations differ in space-time properties and describe several types of massive and corresponding massless particles. In particular we proposed four different equations, which could describe four types of neutrinos.