Invariant Field Equations Research Articles

Covariant extensions and the nonsymmetric unified field

The problem of generally covariant extension of Lorentz invariant field equations, by means of covariant derivatives extracted from the nonsymmetric unified field, is considered. It is shown that the contracted curvature tensor can be expressed in terms of a covariant gauge derivative which contains the gauge derivative corresponding to minimal coupling, if the universal constantp, characterizing the nonsymmetric theory, is fixed in terms of Planck's constant and the elementary quantum of charge. By this choice the spinor representation of the linear connection becomes closely related to the spinor affinity used by Infeld and Van Der Waerden in their generally covariant formulation of Dirac's equation.

Relativistic theory of magnetoelastic interactions. I

The relativistically invariant field equations relevant to mechanics thermodynamics and electromagnetism are presented in a phenomenological continuum theory of magnetoelastic interactions in which the magnetic spin is accounted for.

Invariant Form of the Maxwell-Lorentz Field Equations for Accelerated Systems

It is shown that the invariant field equations of Maxwell for stationary bodies are also valid for accelerated bodies, if all ordinary differentiations are replaced by absolute differentiation. The affine connection Γγαβ appearing in the absolute derivatives refers to a general non-Riemannian metric space, with a holonomic or nonholonomic reference frame. The field equations are in a more general form than those used in the five-dimensional unified field theory and reduce to the latter as a special case. However, the presence of an electrostatic field is not assumed in this paper. The motion of an accelerated body possessing mass, electric current and magnetic flux is given by an extended form of the dynamical equations of Lagrange containing the same general affine connection as the field equations. The material terms of the dynamical equations are expressed by a mechanical impulse-energy tensor and the resultant motion of the material body under the influence of an electromagnetic field and a mechanical force is expressed by a combined impulse-energy equation. The equations are calculated for a representative rotating electrical machine used in industry.