Representations of the Quantum HolonomyDiffeomorphism 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 holonomydiffeomorphism algebra. Since the quantum holonomydiffeomorphism 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 YangMills Hamilton operator. This establishes the existence of a general nonperturbative framework of quantum gauge theories on a curved backgrounds. Questions concerning gaugeinvariance are left open.
 Publication:

arXiv eprints
 Pub Date:
 September 2017
 arXiv:
 arXiv:1709.02943
 Bibcode:
 2017arXiv170902943A
 Keywords:

 Mathematical Physics;
 General Relativity and Quantum Cosmology;
 High Energy Physics  Theory;
 Mathematics  Quantum Algebra
 EPrint:
 28 pages