Gravitational and electroweak unification by replacing diffeomorphisms with larger group

TL;DR

This paper proposes enlarging the covariance group in general relativity to unify gravitational and electroweak interactions, resulting in a non-commutative geometry based on paths, not points, and eliminating arbitrary parameters.

Contribution

It introduces a larger covariance group replacing diffeomorphisms, leading to a unified theory of gravity and electroweak interactions with a nonlocal, path-based geometry.

Findings

Unification of gravity and electroweak interactions.

Development of a non-commutative, path-based geometric framework.

No adjustable parameters in the proposed theory.

Abstract

The covariance group for general relativity, the diffeomorphisms, is replaced by a group of coordinate transformations which contains the diffeomorphisms as a proper subgroup. The larger group is defined by the assumption that all observers will agree whether any given quantity is conserved. Alternatively, and equivalently, it is defined by the assumption that all observers will agree that the general relativistic wave equation describes the propagation of light. Thus, the group replacement is analogous to the replacement of the Lorentz group by the diffeomorphisms that led Einstein from special relativity to general relativity, and is also consistent with the assumption of constant light velocity that led him to special relativity. The enlarged covariance group leads to a non-commutative geometry based not on a manifold, but on a nonlocal space in which paths, rather than points, are the most primitive invariant entities. This yields a theory which unifies the gravitational and electroweak interactions. The theory contains no adjustable parameters, such as those that are chosen arbitrarily in the standard model.