A Weyl-Cartan space-time model based on the gauge principle

Abstract

Based on the requirement that the gauge invariance principle for the Poincare-Weyl group be satisfied for the space-time manifold, we construct a model of space-time with the geometric structure of a Weyl-Cartan space. We show that three types of fields must then be introduced as the gauge (“compensating”) fields: Lorentz, translational, and dilatational. Tetrad coefficients then become functions of these gauge fields. We propose a geometric interpretation of the Dirac scalar field. We obtain general equations for the gauge fields, whose sources can be the energy-momentum tensor, the total momentum, and the total dilatation current of an external field. We consider the example of a direct coupling of the gauge field to the orbital momentum of the spinor field. We propose a gravitational field Lagrangian with gauge-invariant transformations of the Poincare-Weyl group.