TY - BOOK

T1 - On the Classical and Quantum Momentum Map

AU - Esposito, Chiara

PY - 2012

Y1 - 2012

N2 - In this thesis we study the classical and quantum momentum mapsand the theory of reduction. We focus on the notion of momentummap in Poisson geometry and we discuss the classification of themomentum map in this framework. Furthermore, we describe theso-called Poisson Reduction, a technique that allows us to reducethe dimension of a manifold in presence of symmetries implementedby Poisson actions.Using techniques of deformation quantization and quantumgroups, we introduce the quantum momentum map as a deformationof the classical momentum map, constructed in such a waythat it factorizes the quantum action. As an application we discusssome examples of quantum reduction.

AB - In this thesis we study the classical and quantum momentum mapsand the theory of reduction. We focus on the notion of momentummap in Poisson geometry and we discuss the classification of themomentum map in this framework. Furthermore, we describe theso-called Poisson Reduction, a technique that allows us to reducethe dimension of a manifold in presence of symmetries implementedby Poisson actions.Using techniques of deformation quantization and quantumgroups, we introduce the quantum momentum map as a deformationof the classical momentum map, constructed in such a waythat it factorizes the quantum action. As an application we discusssome examples of quantum reduction.

M3 - Ph.D. thesis

BT - On the Classical and Quantum Momentum Map

PB - Faculty of Science, University of Copenhagen

ER -