Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
1996-06-29
Class.Quant.Grav.15:839-873,1998
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
33 pages, Latex, followed by companion paper after this one
Scientific paper
10.1088/0264-9381/15/4/011
An anomaly-free operator corresponding to the Wheeler-DeWitt constraint of Lorentzian, four-dimensional, canonical, non-perturbative vacuum gravity is constructed in the continuum. This operator is entirely free of factor ordering singularities and can be defined in symmetric and non-symmetric form. We work in the real connection representation and obtain a well-defined quantum theory. We compute the complete solution to the Quantum Einstein Equations for the non-symmetric version of the operator and a physical inner product thereon. The action of the Wheeler-DeWitt constraint on spin-network states is by annihilating, creating and rerouting the quanta of angular momentum associated with the edges of the underlying graph while the ADM-energy is essentially diagonalized by the spin-network states. We argue that the spin-network representation is the ``non-linear Fock representation" of quantum gravity, thus justifying the term ``Quantum Spin Dynamics (QSD)".
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