Multivalued functionals and geometrical approach for quantization of relativistic particles and strings

Abstract

The application of the coherent state method combined with the method of orbits to the Feynman path integral formulation of quantum problems with a dynamical symmetry group is presented and used for the quantization of relativistic spinning particles and strings. The action of a spinning string considered as a quantization of the Kac-Moody group based on the Poincaré group is expressed in terms of the extrinsic geometry of the embedding of the surface into the flat space-time. The geometrical quantization and Feynman path integral formulation of some models known in condensed matter physics is also presented.