Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2000-04-04
Nucl.Phys.Proc.Suppl. 88 (2000) 314-317
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
Talk given at Third Conference on Constrained Dynamics and Quantum Gravity, September, 1999. To appear in Nuclear Physics B (P
Scientific paper
10.1016/S0920-5632(00)00792-1
It might seem that a choice of a time coordinate in Hamiltonian formulations of general relativity breaks the full four-dimensional diffeomorphism covariance of the theory. This is not the case. We construct explicitly the complete set of gauge generators for Ashtekar's formulation of canonical gravity. The requirement of projectability of the Legendre map from configuration-velocity space to phase space renders the symmetry group a gauge transformation group on configuration-velocity variables. Yet there is a sense in which the full four-dimensional diffeomorphism group survives. Symmetry generators serve as Hamiltonians on members of equivalence classes of solutions of Einstein's equations and are thus intimately related to the so-called "problem of time" in an eventual quantum theory of gravity.
Pons Josep Maria
Salisbury Donald C.
Shepley L. C.
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