The connection between field-theory and the equations for material sistems

The existing field theories are based on the properties of closed exterior forms, which correspond to conservation laws for physical fields. In the present paper it is shown that closed exterior forms corresponding to field theories are obtained from the equations modelling conservation (balance) laws for material sistems (material media). The process of obtaining closed exterior forms demonstrates the connection between field-theory equations and the equations for material sistems and points to the fact that the foundations of field theories must be conditioned by the properties of equations conservation laws for material sistems. 1. Peculiarities of differential equations for material sistems Equations for material sistems are equations that describe the conservation laws for energy, linear momentum, angular momentum and mass. Such conservation laws can be named as balance ones since they establish the balance between the variation of a physical quantity and corresponding external action. [The material system material (continuous) medium is a variety (infinite) of elements that have internal structure and interact among themselves. Thermodynamical, gasodynamical and cosmologic system, systems of elementary particles and others are examples of material system. (Physical vacuum can be considered as an analog of such material system.) Electrons, protons, neutrons, atoms, fluid particles and so on are examples of elements of material system.] The equations of balance conservation laws are differential (or integral) equations that describe a variation of functions corresponding to physical quantities [1-3]. (The Navier-Stokes equations are an example [3].) It appears that, even without a knowledge of the concrete form of these equations, one can see specific features of these equations and their solutions using skew-symmetric differential forms [4-6]. To do so it is necessary to study the conjugacy (consistency) of these equations. The functions for equations of material sistems sought are usually functions which relate to such physical quantities like a particle velocity (of elements), temperature or energy, pressure and density. Since these functions relate to one material system, it has to exist a connection between them. This connection is described by the state-function. Below it will be shown that the analysis of integrability and consistency of equations of balance conservation laws for material media reduces to a study the nonidentical relation for the state-function. Let us analyze the equations that describe the balance conservation laws for energy and linear momentum.