The Macroscopic Limit of the Poincaré Gauge Field Theory of Gravitation

Abstract

In the framework of the recently1 formulated Poincare gauge field theory of gravitation we study the limit of macroscopic spinless matter modelled by a scalar matter field ϕ. We define local active Poincare transformations for scalar matter and the corresponding invariance. We derive a Yang-Mills-type tetrad field equation and assume the gauge field Lagrangian to be quadratic in torsion. In order to find a definitive “viable” field Lagrangian, we investigate the weak field approximation. We discuss groups of motions in a U4 with vanishing curvature \(\left( {F\begin{array}{*{20}{c}}{ \bullet \bullet \bullet } \\ {i j \alpha } \end{array}\beta = {\rm O}} \right)\) and prove, among other things, that (i) all spherical symmetric solutions of the Poincare gauge field theory for macroscopic matter (translational gauge field theory) are also solutions in Einstein’s theory and vice versa; (ii) in fifth order of the post-Newtonian approximation there is a deviation from Einstein’s theory. This deviation shows up in the spin precession of a Dirac test particle moving in the gravitational field of a rotating body.