Connection between functionals of the field-theory equations and state functionals of the mathematical physics equations

Abstract

It is well known that the field-theory equations are equations for such functionals as the action functional, entropy, Pointing's vector, Einstein's tensor, wave function, and others. It turns out that the equations of mathematical physics describing material systems (material media) such as the thermodynamic, gas-dynamic and cosmic systems as well as the systems of charged particles and others can be expressed in terms of the same functionals. Such a duality of functionals points out to a connection between the field-theory equations, which describe physical fields, and the mathematical physics equation, which describe material media. This discloses a connection of physical fields and material media.