On the Natural Gauge Fields of Manifolds

TL;DR

This paper explores the gauge symmetry of manifolds, deriving invariant equations for the displacement field, and demonstrates that such fields can transport energy and gravitate, with specific spherically symmetric solutions in Minkowski space-time.

Contribution

It introduces a natural gauge field on manifolds and derives gauge-invariant equations, showing their physical significance and solutions in Minkowski space.

Findings

Displacement field can transport energy and gravitate.

Gauge-invariant equations for the displacement field are derived.

Spherically symmetric solutions are found in Minkowski space.

Abstract

The gauge symmetry inherent in the concept of manifold has been discussed. Within the scope of this symmetry the linear connection or displacement field can be considered as a natural gauge field on the manifold. The gauge invariant equations for the displacement field have been derived. It has been shown that the energy-momentum tensor of this field conserves and hence the displacement field can be treated as one that transports energy and gravitates. To show the existence of the solutions of the field equations we have derived the general form of the displacement field in Minkowski space-time which is invariant under rotation and space and time inversion. With this anzats we found spherically-symmetric solutions of the equations in question.