- IRAP Lectures 2006 (April-June)

GEOMETRODYNAMICS AND MATTER FIELDS (By Dr. Giovanni Montani)

Aim of the lectures is to analyse the links existing between Gravity and other Fundamental Interactions. We start by reviewing features of Quantum Fields Theory and then we present Gravity in the framework of a Gauge Theory; finally, the open problems in Quantum Gravity are discussed in some details.

1. QUANTUM FIELDS THEORY: Symmetries of the Minkowski spacetime, Fundamental physical fields, Second quantization and the S-matrix, Generating functional, Gauge theories, Spontaneous symmetry breaking, Higgs phenomenon, On the Standard Model

2. CLASSICAL GEOMETRODYNAMICS: General Relativity as a gauge theory, Hamiltonian approach, Constraints algebra, Hamilton-Jacobi equation, Ashtekar variables, Cosmological dynamics, Torsion field, Kaluza-Klein theories

3. QUANTUM GRAVITY: Matter fields on curved spacetime, Quantum field theory on curved spacetime, Canonical quantum gravity, Problem of time, Multi-time approach, Path integral formulation, Evolutionary quantum gravity, Quantum cosmology, Generalized uncertainty principle