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

Abstract

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 WeylCartan 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.

The “Gravity Probe B” experiment, interaction between the orbital moment and gauge field, and a gravidiamagnetic effect

“…This difficulty was overcome in a new variant of the Poincaré-gauge gravitation theory [4,5] and a recently developed Poincaré-Weyl-gauge gravitation theory [6,7], where the angular momentum The theory is developed on the basis of the Noether theorems allowing gauge fields dynamically realizing the laws of conservation of energy-momentum, total rotational moment (orbital and spin), and dilatation charge to be introduced. The dilatation charge is due to the invariance of the theory with respect to tension and compression of spacetime.…”

“…In [6,7], discussed is the case where a spinor field plays the role of external one. The Lagrange density of interaction with the gauge field of the Poincaré-Weyl group is written as , .…”

“…Let us calculate the foregoing additional, as compared with standard GRT, interaction in the Lagrangian [7]. Calculations for the spinor field of the energy-momentum tensor result in…”

“…In the absence of action upon the orbital moment, the orbit plane will take up a constant position in space. Under fairly slow action of the Lorentz gauge field upon the orbital moment, precession of the orbit will take place [7]. This phenomenon will be perceived as a change in diamagnetic properties of matter, therefore, we can assume that this effect can be used for detecting gravitational and torsional waves.…”

The use of symbolic calculations in post-Riemannian and multidimensional theories of gravity

“…These identities were taken from the monograph [10] where a theory of gravity was studied without introducing a scalar field. However, as shown in [11][12][13], from the requirements of the Poicar´e-Weyl gauge theory of gravity follows the necessity of introducing a scalar field as an additional component of the metric tensor. The properties of this field coincide with those of the scalar field introduced by Dirac [14].…”