  It is shown that there is a correspondence between field theory equations
such as the Dirac, Shr\H{o}dinger, Maxwell, Einstein equations and closed
exterior forms of a certain degree. In this case, the Dirac and Shr\H{o}dinger
equations for the wave function correspond to closed exterior forms of zero
degree. The Shr\H{o}dinger equation for the state functional corresponds to
closed exterior forms of the first degree. The Maxwell's equations based on
exterior forms of second degree. Einstein's equation for the gravitational
field consists of covariant tensors, which correspond to closed exterior forms
of the second degree. However, the covariant tensors of the Einstein equation
are derived from the covariant tensors, which correspond to closed exterior
forms of third degree. Such a correspondence between the field theory equations
and closed exterior forms of a certain degree reveals the internal connection
between the field theory equations. At the same time, it was shown that closed
exterior forms, on which the field theory equations for physical fields are
based, are associated with the equations of mathematical physics for material
media, such as thermodynamic, gas-dynamic, electromagnetic, cosmological
equations, etc.
  This indicates the connection between the field theory equations and the
mathematical physics equations and reveals the foundations of field theory.
