Invariants in electromagnetic and gravitational adjoint fields
  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. 
Zihua Weng