Given Lectures

- 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 the framework of a Gauge Theory and the open problems in Quantum Gravity  will be discussed in some detail. THE LECTURES STARTED ON FEBRUARY 6, 2007.

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
  

 
        
- 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
        
 
        
 
        
- IRAP Lectures 2005 
        
...