Physics
Scientific paper
Dec 2002
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2002nmgm.meet.1038k&link_type=abstract
"THE NINTH MARCEL GROSSMANN MEETING On Recent Developments in Theoretical and Experimental General Relativity, Gravitation and R
Physics
Scientific paper
The main motivation to study general dilaton theories comes from spherically reduced gravity (SRG) 1 or string theory 2,3, although the dilaton black hole has a null-complete singularity 4. Previous studies of general dilaton theories 5 in the conformal gauge only could treat quantum theory in a semiclassical way 6 through the addition of the Polyakov action 7. For the example of a 2d model with torsion 8,9 the crucial advantages of a physical gauge 10 like the light cone gauge for the Cartan variables 11,12 were realised which, for that model, even allowed an exact path integral 13 and exact Dirac quantization 14. Because the light cone gauge for Cartan variables implies Eddington-Finkelstein gauge for the metric the global features of all 2d theories could be analysed in great detail 15. Motivated by the Hamiltonian analysis 16 and an analogous formulation in string theory 17 the importance of a first order formulation 18 was realized because of its local and global equivalence to the usual formulation as a dilaton theory 14,19. Even in the presence of matter 20 an absolute conservation law, generalizing the notion of the ADM-mass 21 to an energy flux relation 22 and a related novel type of Noether symmetry 23 were found. The concept of the "Poisson-Sigma-Model" 24 emerged in this context which now also finds an application in string theory 25 and can be used to create all possible 2d supergravity theories 26,27. The main power of the first order formulation was noticed in connection with the path integral formulation of 2d gravity where matter can be included by systematic loop-wise expansion 19. Based upon the formalism of extended Hamilton theory 28 with contributions to the constraints also including fermions 29 it was shown recently 30 that as one of the results of 2d quantum gravity a "virtual black hole" appears in the scattering of scalars. Planned applications include reduced generalized Einstein theories 31.
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