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arXiv · 1709.02943

Representations of the Quantum Holonomy-Diffeomorphism Algebra

Johannes Aastrup·Jesper M. Grimstrup
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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.

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Johannes Aastrup, Jesper M. Grimstrup. 2017-09-09. Representations of the Quantum Holonomy-Diffeomorphism Algebra. https://arxiv.org/abs/1709.02943

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