1. Poincare symmetry Poincare transformations. Lie algebra and its representations. Invariance of the action and conservation laws. 2. Conformal symmetry Conformal transformations and Weyl rescaling. Lie algebra and finite transformations. Conserved currents. Conformal transformations in D=2. 3. Poincare gauge invariance Localization of Poincare symmetry. Conservation laws. 4. Geometric interpretation of PGT Riemann-Cartan space U(4). Geometric and gauge structure of PGT. The principle of equivalence in PGT. 5. Gravitational dynamics Einstein-Cartan theory. Teleparallel theory. 6-7. Constrained Hamiltonian dynamics Introduction to Dirac's theory. Generators of gauge symmetries. Electrodynamics. 8-9. Gravitational Hamiltonian Covariance and Hamiltonian dynamics. Primary constraints. The (3+1) decomposition os spacetime. Construction of the Hamiltonian. Consistency of the theory and gauge conditions. 10. Einstein-Cartan theory. Teleparallel theory. 11. Gauge symmetries Constraint algebra. Gauge generators. 12. Conservation laws - EC theory Asymptotic structure of spacetime. Improving the Poincare generators. 13. Chern-Simons theory in D=3 Action. Canonical analysis. Symmetries at the boundary. 14. Chern-Simons gravity in D=3 GR as a CS theory. Adding a cosmological constant. More on CS formulation. The AdS space.
Requirements include: 80 homework exercises, 2 seminars, The course Gravitation 1 Literature: M. Blagojevic, Gravitation and Gauge Symmetries, chapters 2,3,5,6, appendix L, and references therein.
