Duality of gravitation in the quantization problem

Gravitational pseudoparticles are considered in the framework of the gauge treatment of gravitation. The investigation is based on de Rham's duality theorem, which establishes the periods of the curvature form as the associated topological charges. It is assumed that the gravitational fields satisfy a gauge condition that distinguishes fields of Abelian type. Necessary and sufficient conditions for the existence of gravitational pseudoparticles are stated and examined. In the framework of the specified gauge, the analogy with Yang–Mills fields corresponding to an Abelian group is studied.