Title: Geometric Quantization and Its Application In AdS3 Gravity
Presenter: Mahboube Abbasi (FUM)
Time & Date: 10:00 IRST - July 31st, 2024
Location: Ferdowsi University, Faculty of Science, Room 14
Abstract: Quantization is an important theme in many areas of mathematics and physics. Geometric quantization aims to associate to any classical phase space, modeled by a symplectic manifold, a quantum space, modeled by a Hilbert space. A relevant feature of geometric quantization is its close relationship with the theory of irreducible unitary representations of Lie groups. In fact, by the geometric quantization process of coadjoint orbits of a given Lie group, one can obtain its irreducible unitary representations which is known as the orbit method.
In this thesis, by using this method, we describe irreducible unitary representations of Poincaré and Galilean groups which are known as relativistic and non-relativistic particles, respectively. Then we study the Virasoro group which is a part of the asymptotic symmetry group of many gravitational systems and two-dimensional conformal field theories.