- IRAP Lectures 2007 (February-April)

FROM CLASSICAL TO QUANTUM GRAVITY (By Dr. Giovanni Montani)

Aim of the lectures is to analyze the links existing between Einsteinian Gravity and Quantum Physics. We will start with reviewing the fundamental features concerning classical Geometrodynamics and Quantum Field Theory. Then we will present Gravity in a Gauge Theory framework, and the open problems in Quantum Gravity will be discussed in some detail.

1. CLASSICAL GEOMETRODYNAMICS: Differential manifolds, Einsteinian gravity, Cauchy problem, Hamiltonian approach, Constraints algebra, Hamilton-Jacobi equation, Formulation of a generic cosmological problem

2. QUANTUM FIELDS THEORY: Fundamental physical fields, Second quantization
and the S-matrix, Generating functional, Gauge Theories, Spontaneous symmetry 
breaking, Higgs phenomenon

3. QUANTUM GRAVITY: Matter fields on curved space-time, Constraints quantization,
Canonical quantum gravity, Problem of time, Multi-time approach, Path integral
formulation, Evolutionary quantum gravity, Quantum cosmology, Gravity as a gauge 
theory, Ashtekar variables, Loop quantum gravity, Generalized uncertainty principle