Sedeonic theory of massless fields

TL;DR

This paper introduces a sedeonic algebra framework to describe massless fields, proposing unified equations for gravitoelectromagnetism and neutrino fields, and deriving related energy, momentum, and invariant relations.

Contribution

It develops a novel sedeonic algebra approach to unify gravitoelectromagnetic and neutrino fields within a single mathematical framework.

Findings

Derived second-order equations for gravitoelectromagnetic fields.

Established relations for energy, momentum, and invariants in the sedeonic framework.

Formulated first-order equations for neutrino fields with analogous invariant relations.

Abstract

In present paper we develop the description of massless fields on the basis of space-time algebra of sixteen-component sedeons. The generalized sedeonic second-order equation for unified gravitoelectromagnetic (GE) field describing simultaneously gravity and electromagnetism is proposed. The second-order relations for the GE field energy, momentum and Lorentz invariants are derived. We consider also the generalized sedeonic first-order equation for the massless neutrino field. The second-order relations for the neutrino potentials analogues to the Pointing theorem and Lorentz invariant relations in gravitoelectromagnetism are also derived.