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arXiv · 1602.06436

On a Lattice-Independent Formulation of Quantum Holonomy Theory

Johannes Aastrup·Jesper M. Grimstrup
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Abstract

Quantum holonomy theory is a candidate for a non-perturbative theory of quantum gravity coupled to fermions. The theory is based on the QHD(M) algebra, which essentially encodes how matter degrees of freedom are moved on a three-dimensional manifold. In this paper we commence the development of a lattice-independent formulation. We first introduce a flow-dependent version of the QHD(M) algebra and formulate necessary conditions for a state to exist hereon. We then use the GNS construction to build a kinematical Hilbert space. Finally we find that operators, that correspond to the Dirac and gravitational Hamiltonians in a semi-classical limit, are background independent.

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Johannes Aastrup, Jesper M. Grimstrup. 2016-04-11. On a Lattice-Independent Formulation of Quantum Holonomy Theory. https://doi.org/10.1088/0264-9381%2F33%2F21%2F215002

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