2 00 8 Two types of conservation laws . Connection of physical fields with material systems . Peculiarities of field theories

Historically it happen so that in branches of physics connected with field theory and of physics of material systems (continuous media) the concept of ”conservation laws” has a different meaning. In field theory ”conservation laws” are those that claim the existence of conservative physical quantities or objects. These are conservation laws for physical fields. In contrast to that in physics (and mechanics) of material systems the concept of “conservation laws” relates to conservation laws for energy, linear momentum, angular momentum, and mass that establish the balance between the change of physical quantities and external action. In the paper presented it is proved that there exist a connection between of conservation laws for physical fields and those for material systems. This points to the fact that physical fields are connected with material systems. Such results has an unique significance for field theories. This enables one to substantiate many basic principles of field theories, such as, for example, the unity of existing field theories and the causality. The specific feature of field theory equations, namely, their connection to the equations for material systems, is elicited. Such results have been obtained by using skew-symmetric differential forms, which reflect the properties of conservation laws. (It appears to be possible to obtain radically new results due to using skew-symmetric differential form, which, in contrast to exterior forms, are defined on nonintegrable manifolds and possesses evolutionary properties. The mathematical apparatus of evolutionary forms includes nontraditional elements, that are, nonidentical relations and degenerate transformations. This enables one to describe the mechanism of arising and generating the structures that is impossible to perform within the framework of any existing mathematical formalisms. The existence of such skewsymmetric differential forms has been established by the author while studying the stability problems.) 1 Meaning of the concept of “conservation laws” Due to the development of science the concept of “conservation laws” in thermodynamics, physics and mechanics contains different meanings. In branches of physics related to field theory and in theoretical mechanics “the conservation laws” are those according to which there exist conservative physical quantities or objects. These are the conservation laws that were called above as “exact” ones. In mechanics and physics of continuous media the concept of “conservation laws” relates to conservation laws for energy, linear momentum, angular mo-