Syllabus
Einstein-Cartan-Palatini-Holst Lagrangian and equations of motion.
Hamilton analysis of Einstein-Cartan-Palatini-Holst Lagrangian - ADM formalism.
RAQ - Summary of general algebraic approach to quantization of systems with constraints.
Basic loop variables and their representation.
Volume and Area operators.
Annotation
Loop Quantum Gravity is one of the candidates for the theory of quantum gravity, which is background independent and does not require renormalization. The main aim of these lectures is to understand its kinematical formulation.
Starting from the Einstein-Palatini-Holst Lagrangian we perform its classical Hamiltonian analysis. Ashtekar variables and Loop representation are introduced.
Dirac’s approach to constrained systems and Algebraic Quantization are employed. Volume and Area operators possessing discrete spectra are constructed.
Intended for advanced graduate and postgraduate students.