Quantum Spin Dynamics (QSD)

TL;DR

This paper constructs a consistent, anomaly-free quantum operator for Lorentzian vacuum gravity in four dimensions, providing a complete solution to the Quantum Einstein Equations within the spin-network framework, and introduces Quantum Spin Dynamics as a non-linear Fock representation of quantum gravity.

Contribution

It introduces a new anomaly-free operator for quantum gravity, solves the Quantum Einstein Equations explicitly, and establishes the spin-network representation as a non-linear Fock space.

Findings

Operator is free of factor ordering singularities.

Complete solutions to Quantum Einstein Equations are obtained.

Spin-network states diagonalize ADM-energy and act as a non-linear Fock space.

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)".