On pseudoparticle solutions in the poincaré gauge theory of gravity

Abstract

AbstractThe dynamical structure of the Poincaré gauge field theory coupled to matter fields and some of its implications for a quantum theory of gravity are investigated.Essentially, the method of BELAVIN et al. for generating instanton solutions in Yang‐Mills theory is transferred to the gravitational gauge model. The result are as follows: For configurations obeying a modified double duality Ansatz for the curvature the metrical background is determined by Einstein‐type field equations coupled almost canonically to the stress‐energy content of external fields.Exact electrovac solutions with non‐trivial torsion are derived from the duality Ansatz. In a Euclidean space‐time the corresponding pseudoparticle solutions are expected to play a dominant rǒle in the quantization of gravity via Freynman's method of path integrals.