REMARKS CONCERNING THE GEOMETRIES OF GRAVITY AND GAUGE FIELDS

TL;DR

This paper discusses fundamental differences between gravity and gauge fields, emphasizing the role of the solder form in space-time geometry and its implications for quantization approaches.

Contribution

It highlights the significance of the solder form over the metric in the quantization of gravity and clarifies the geometric distinctions from gauge fields.

Findings

The analogy between the Aharonov-Bohm effect and parallel transport on a cone has limitations.

The solder form is essential in understanding space-time geometry and gravity.

Gravitational phase observability for open paths supports alternative quantization variables.

Abstract

An important limitation is shown in the analogy between the Aharonov-Bohm effect and the parallel transport on a cone. It illustrates a basic difference between gravity and gauge fields due to the existence of the solder form for the space-time geometry. This difference is further shown by the observability of the gravitational phase for open paths. This reinforces a previous suggestion that the fundamental variables for quantizing the gravitational field are the solder form and the connection, and not the metric.