Skew-symmetric differential forms: Conservation laws and symmetries

Abstract:
Skew-symmetric differential forms enables one to understand the meaning of conservation laws. The closure condition for exterior form and dual form describes conservation laws for physical fields. In this paper the differential forms, whose basis are nondifferentiable manifolds, are used. These forms are connected with conservation laws for material media and possess the evolutionary properties. Transition from the evolutionary forms to closed exterior forms is transition from conservation laws for material media to conservation laws for physical fields. The conditions of this transition are connected with symmetries, which can be due to the degrees of freedom of material media.