**
**### Gravitation 2

The course consists of 14 lectures (90 minutes each).
Instructor: M. Blagojevic

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.