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

TL;DR

This paper explores the connection between conservation laws in physical fields and material systems, revealing their interdependence and implications for the foundational principles of field theories using skew-symmetric differential forms.

Contribution

It establishes a link between conservation laws in field theory and material systems, providing a new perspective on the unity and causality in field theories.

Findings

Physical fields are connected with material systems.

Conservation laws in fields relate to those in material systems.

Results support the unity and causality principles in field theories.

Abstract

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.