On a Lattice-Independent Formulation of Quantum Holonomy Theory
General Relativity and Quantum Cosmology
2016-10-19 v2 High Energy Physics - Theory
Mathematical Physics
math.MP
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.
Keywords
Cite
@article{arxiv.1602.06436,
title = {On a Lattice-Independent Formulation of Quantum Holonomy Theory},
author = {Johannes Aastrup and Jesper M. Grimstrup},
journal= {arXiv preprint arXiv:1602.06436},
year = {2016}
}
Comments
22 pages, 1 figure. Title and section on Dirac operator changed