Gauge field theory for Poincar\'{e}-Weyl group

TL;DR

This paper develops a gauge field theory for the Poincaré-Weyl group, revealing new interactions and geometrical structures, including Weyl-Cartan spacetime and a dilaton field interpreted as part of the tangent space metric.

Contribution

It constructs a gauge theory for the Poincaré-Weyl group, showing tetrads are functions of true gauge fields and introducing a new interaction with orbital momentum.

Findings

Tetrads are functions of Lorentzian, translational, and dilatational gauge fields.

A new interaction between Lorentzian gauge field and orbital momentum is identified.

Spacetime is described as a Weyl-Cartan space with a dilaton field as a tangent space metric component.

Abstract

On the basis of the general principles of a gauge field theory the gauge theory for the Poincar\'{e}-Weyl group is constructed. It is shown that tetrads are not true gauge fields, but represent functions from true gauge fields: Lorentzian, translational and dilatational ones. The equations of gauge fields which sources are an energy-momentum tensor, orbital and spin momemta, and also a dilatational current of an external field are obtained. A new direct interaction of the Lorentzian gauge field with the orbital momentum of an external field appears, which describes some new effects. Geometrical interpretation of the theory is developed and it is shown that as a result of localization of the Poincar\'{e}-Weyl group spacetime becomes a Weyl-Cartan space. Also the geometrical interpretation of a dilaton field as a component of the metric tensor of a tangent space in Weyl-Cartan geometry is proposed.