Dark Matter and Potential fields

TL;DR

This paper introduces a geometrical framework for dark matter as a potential field, linking it to electromagnetic theory, and explores its interactions with matter through a generalized covariant Dirac equation.

Contribution

It proposes a new geometrical interpretation of dark matter as a potential field, deriving invariant equations and connecting them to electromagnetic and Dirac equations.

Findings

Dark matter field can be described as a generalized electromagnetic field.

Gauge fixing makes the generalized electromagnetic field effectively massive.

Derived a covariant Dirac equation describing spinor interactions with dark matter.

Abstract

A general concept of potential field is introduced. The potential field that one puts in correspondence with dark matter, has fundamental geometrical interpretation (parallel transport) and has intrinsically inherent in local symmetry. The equations of dark matter field are derived that are invariant with respect to the local transformations. It is shown how to reduce these equations to the Maxwell equations. Thus, the dark matter field may be considered as generalized electromagnetic field and a simple solution is given of the old problem to connect electromagnetic field with geometrical properties of the physical manifold itself. It is shown that gauge fixing renders generalized electromagnetic field effectively massive while the Maxwell electromagnetic field remains massless. To learn more about interactions between matter and dark matter on the microscopical level (and to recognize the fundamental role of internal symmetry) the general covariant Dirac equation is derived in the Minkowski space--time which describe the interactions of spinor field with dark matter field.