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

Based on the requirement that the gauge invariance principle for the Poincaré–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 Poincaré–Weyl group.