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Quantum Spin Dynamics (QSD)

T. Thiemann
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Abstract

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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T. Thiemann. 1996-06-29. Quantum Spin Dynamics (QSD). https://doi.org/10.1088/0264-9381%2F15%2F4%2F011

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