Four lectures on Poincare gauge field theory
Abstract
The Poincare (inhomogeneous Lorentz) group underlies special relativity. A consistent formalism is developed to allow an appropriate gauging of the Poincare group. The physical laws are formulated in terms of points, orthonormal tetrad frames, and components of the matter fields with respect to these frames. The laws are postulated to be gauge invariant under local Poincare transformations. This implies the existence of 4 translational gauge and 6 Lorentz gauge potentials and the coupling of the momentum current and the spin current of matter to these potentials, respectively. Thus, a path is led to a RiemannCartan spacetime carrying torsion and curvature, richer in structure than the space time of general relativity. The RiemannCartan space time is controlled by the two general gauge field equations, in which material momentum and spin act as sources. The general framework of the theory is summarized in a table. Options for picking a gauge field Lagrangian are discussed. A Lagrangian quadratic in torsion and curvature governing the propagation of gravitons and rotons is proposed. A suppression of the rotons leads back to general relativity.
 Publication:

Presented at the Intern. School of Cosmology and Gravitation
 Pub Date:
 December 1979
 Bibcode:
 1979cogr.conf.....H
 Keywords:

 Poincare Problem;
 Points (Mathematics);
 Relativity;
 Gauge Invariance;
 Gravitons;
 Orthonormal Functions;
 Thermodynamics and Statistical Physics