Romanenko A. Application of Scwinger’s action principle to quantization of systems on curved manifolds.

Thesis is devoted to the investigation of the structure of the quantum mechanics on the noneuclidean space and learning the features of the particle-like configurations in Volkov-Akulov model with nonlinear realization of the supersymmetry. Generalization of Schwinger's quantum action principle is considered. In this approach the influence of geometry on the character of a quantum theory can be taken into account correctly.For the analyzes the different types of the manifolds are chosen. we consider homogeneous and general Riemannian manifolds and a supermanifold.The methods developed for the quantum-mechanical problems have been applied for Volkov-Akulov field model with non-linear realization of supersymmetry.In this model the essentially quantum solution was found. Its character size is equal to the Planck length. It was shown that the external field interacting with this object is not singular at the origin.Such a non-linear field configuration can be considered as a model of an elementary charge.