1996/06/29 by T. Thiemann · 1 citation
Physics and Astronomy · #gr-qc #hep-th
paper · pdf · doi:10.1088/0264-9381/15/4/011
published as Class.Quant.Grav.15:839-873,1998 · 33 pages, Latex, followed by companion paper after this one
arxiv created 1996/06/29 · arxiv updated 2009/11/30
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)".