Foundations of the field theory: Connection of the field-theory equations with the equations of mathematical physics

Petrova L.I.

Moscow State University, Department of Computational Mathematics and Cybernetics, Moscow, Russia

E-mail: Petrova ptr@cs.msu.su

It is known that the equations of mathematical physics for material systems (material media) such as the thermodynamical, gas-dynamical, cosmologic systems, the systems of charged particles and others consist of the equations of conservation laws for energy, linear momentum, angular momentum, and mass.

It turns out that the mathematical physics equations for material systems possess some hidden properties that are manifested only under investigation the consistency of the conservation law equations. Under such investigation one obtains a relation in skew-symmetrical differential forms for the functionals such as the action functional, entropy, Pointing's vector, Einstein's tensor, wave function and other. As it is known, the field-theory equations, which describe physical fields, are equations for such functionals. And this emphasizes the correspondence between the field-theory equations and the relation obtained.

Such a relation, which appears to be evolutionary, nonidentical and self-varying, discloses the connection between the field-theory equations, which describe physical fields, and the equations of mathematical physics, which describe material media. The connection of the field-theory equations with the equations of mathematical physics and the correspondence between the field-theory equations and the evolutionary relation enables one to understand the basic principles of field theory and the properties of physical fields.

The present investigation was carried out with the help of skew-symmetric differential forms, which properties correspond to the conservation laws that lie at the basis of the equations of mathematical physics and the field-theory equations. In doing so, the skew-symmetric forms, which possess some peculiarities, were used. Namely, they are evolutionary ones and can generate closed exterior forms corresponding to the conservation laws for physical fields.

Keywords: material media, evolutionary relation, conservation laws, properties of the field theory.

DOI: 10.18698/2309-7604-2015-1-409-421

Article file: Petrova.pdf