Gauge Freedom and Relativity: A Unified Treatment of Electromagnetism, Gravity and the Dirac Field

TL;DR

This paper presents a unified gauge-theoretic framework for electromagnetism, gravity, and the Dirac field, reinterpreting geometric properties as nonlinear interactions on a flat background, and introduces dynamic proto-gravity fields to generate physical metrics.

Contribution

It introduces a novel gauge approach that treats all fundamental fields on equal footing, promoting Dirac matrices to dynamic fields and enlarging the gauge group for a unified description.

Findings

Proto-gravity fields generate a well-defined physical metric.

Conservation laws are derived from an enlarged gauge symmetry.

Distinction between background-induced and observed quantities is clarified.

Abstract

The geometric properties of General Relativity are reconsidered as a particular nonlinear interaction of fields on a flat background where the perceived geometry and coordinates are "physical" entities that are interpolated by a patchwork of observable bodies with a nonintuitive relationship to the underlying fields. This more general notion of gauge in physics opens an important door to put all fields on a similar standing but requires a careful reconsideration of tensors in physics and the conventional wisdom surrounding them. The meaning of the flat background and the induced conserved quantities are discussed and contrasted with the "observable" positive definite energy and probability density in terms of the induced physical coordinates. In this context, the Dirac matrices are promoted to dynamic proto-gravity fields and the keeper of "physical metric" information. Independent sister fields to the wavefunctions are utilized in a bilinear rather than a quadratic lagrangian in these fields. This construction greatly enlarges the gauge group so that now proving causal evolution, relative to the physical metric, for the gauge invariant functions of the fields requires both the stress-energy conservation and probability current conservation laws. Through a Higgs-like coupling term the proto-gravity fields generate a well defined physical metric structure and gives the usual distinguishing of gravity from electromagnetism at low energies relative to the Higgs-like coupling. The flat background induces a full set of conservation laws but results in the need to distinguish these quantities from those observed by recording devices and observers constructed from the fields.