Invariants in electromagnetic and gravitational adjoint fields

TL;DR

This paper explores how adjoint fields, analyzed through octonions, subtly alter conservation laws in electromagnetic and gravitational fields, affecting mass, charge, and spin conservation.

Contribution

It introduces a novel octonion-based framework to analyze the influence of adjoint fields on fundamental conservation laws in physics.

Findings

Adjoint fields cause slight deviations from conservation laws.

Electromagnetic adjoint fields affect mass conservation.

Gravitational adjoint fields influence charge conservation.

Abstract

The paper discusses the impact of adjoint fields on the conservation laws in the gravitational field and electromagnetic field, by means of the characteristics of octonions. When the adjoint field can not be neglected, it will cause the predictions to departure slightly from the conservation laws, which include mass continuity equation, charge continuity equation, and conservation of spin. The adjoint field of electromagnetic field has an effect on conservation of mass, and that of gravitational field on conservation of charge. The inferences explain how the adjoint field influences some conservation laws in the gravitational field and electromagnetic field.