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The paper discusses the impact of adjoint fields on the conservation laws inthe gravitational field and electromagnetic field, by means of thecharacteristics of octonions. When the adjoint field can not be neglected, itwill cause the predictions to departure slightly from the conservation laws,which include mass continuity equation, charge continuity equation, andconservation of spin. The adjoint field of electromagnetic field has an effecton conservation of mass, and that of gravitational field on conservation ofcharge. The inferences explain how the adjoint field influences someconservation laws in the gravitational field and electromagnetic field.

Invariants in electromagnetic and gravitational adjoint fields