Hamiltonian Approach to 2+1 Dimensional Gravity

Details Hamiltonian Approach to 2+1 Dimensional Gravity Hamiltonian Approach to 2+1 Dimensional Gravity

Dec 2002

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2002nmgm.meet..779c&link_type=abstract

"THE NINTH MARCEL GROSSMANN MEETING On Recent Developments in Theoretical and Experimental General Relativity, Gravitation and R

Physics

Scientific paper

It is shown that the reduced particle dynamics of 2+1 dimensional gravity in the maximally slicing gauge has hamiltonian form. We give the exact diffeomorphism which transforms the spinning cone metric in the Deser, Jackiw, 't Hooft gauge to the maximally slicing gauge. It is explicitly shown that the boundary term in the action, written in hamiltonian form gives the hamiltonian for the reduced particle dynamics. The quantum mechanical translation of the two particle hamiltonian gives rise to the logarithm of the Laplace-Beltrami operator on a cone whose angular deficit is given by the total energy of the system irrespective of the masses of the particles thus proving at the quantum level a conjecture by 't Hooft on the two particle dynamics.

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