Quantum spin dynamics (QSD)

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. 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 `nonlinear Fock representation' of quantum gravity, thus justifying the term `quantum spin dynamics (QSD)'. This paper is the first in a series of seven papers with the title `quantum spin dynamics (QSD)'.