Marc HENNEAUX (Université Libre de Bruxelles & International Solvay Institutes, Brussels, Belgium)

Hamiltonian Formalism of General Relativity

2 lectures: 6, 7 November 2006

Recommended reading

General reading
C.W. Misner, K.S. Thorne and J.A. Wheeler, Gravitation, Freeman (San Francisco 1973), chapter 21.

Original papers
1)The Theory of gravitation in Hamiltonian form.
Paul A.M. Dirac (Cambridge U.) . Mar 1958.
Published in Proc.Roy.Soc.Lond.A246:333-343,1958.
2)The Dynamics of general relativity.
R. Arnowitt (Syracuse U.) , S. Deser (Brandeis U.) , C.W. Misner (Princeton U.) . 1962. 30pp.
Gravitation: an introduction to current research, Louis Witten ed. (Wilew 1962), chapter 7, pp 227-265.
e-Print Archive: gr-qc/0405109
3)Geometrodynamics Regained.
S.A. Hojman, K. Kuchar, C. Teitelboim (Princeton U.) . 1976.
Published in Annals Phys.96:88-135,1976

Hamiltonian treatment of surface integrals (asymptotically Minkowski spaces)
Role Of Surface Integrals In The Hamiltonian Formulation Of General Relativity.
Tullio Regge (Princeton, Inst. Advanced Study) , Claudio Teitelboim (Princeton U.) . Print-74-0988 (IAS,PRINCETON), Mar 1974. 60pp.
Published in Annals Phys.88:286,1974.

Hamiltonian treatment of surface integrals in asymptotocally AdS spaces
1)Stability Of Gravity With A Cosmological Constant.
L.F. Abbott, S. Deser (CERN) . CERN-TH-3136, Aug 1981. 24pp.
Dedicated to Andrei D. Sakharov on his 60th Birthday.
Published in Nucl.Phys.B195:76,1982.
2)Asymptotically Anti-De Sitter Spaces.
M. Henneaux, C. Teitelboim (Texas U. & Chile U., Santiago) . 1985.
Published in Commun.Math.Phys.98:391-424,1985.

More on surface integrals (central charges, algebra)
1)Central Charges In The Canonical Realization Of Asymptotic Symmetries: An Example From Three-Dimensional Gravity.
J.David Brown, M. Henneaux (Texas U.) . 1986.
Published in Commun.Math.Phys.104:207-226,1986.
2)On The Poisson Brackets Of Differentiable Generators In Classical Field Theory.
J.David Brown (Texas U.) , M. Henneaux (Brussels U. & Chile U., Santiago) . 1986.
Published in J.Math.Phys.27:489-491,1986.