Representations of the Quantum Holonomy-Diffeomorphism Algebra
Abstract
In this paper we continue the development of Quantum Holonomy Theory, which is a candidate for a fundamental theory, by constructing separable strongly continuous representations of its algebraic foundation, the quantum holonomy-diffeomorphism algebra. Since the quantum holonomy-diffeomorphism algebra encodes the canonical commutation relations of a gauge theory these representations provide a possible framework for the kinematical sector of a quantum gauge theory. Furthermore, we device a method of constructing physically interesting operators such as the Yang-Mills Hamilton operator. This establishes the existence of a general non-perturbative framework of quantum gauge theories on a curved backgrounds. Questions concerning gauge-invariance are left open.
Cite
@article{arxiv.1709.02943,
title = {Representations of the Quantum Holonomy-Diffeomorphism Algebra},
author = {Johannes Aastrup and Jesper M. Grimstrup},
journal= {arXiv preprint arXiv:1709.02943},
year = {2020}
}
Comments
28 pages