On the Fermionic Sector of Quantum Holonomy Theory

TL;DR

This paper advances quantum holonomy theory by extending the Hilbert space representation to include many-particle states, building on the algebraic framework involving gauge fields and non-commutative geometry.

Contribution

It introduces an extension of the Hilbert space representation in quantum holonomy theory to accommodate many-particle states, enhancing the theory's completeness.

Findings

Extended the Hilbert space to include many-particle states.

Confirmed the algebraic structure supports multi-particle quantum states.

Built upon the spectral triple and Bott-Dirac operator framework.

Abstract

In this paper we continue the development of quantum holonomy theory, which is a candidate for a fundamental theory based on gauge fields and non-commutative geometry. The theory is build around the QHD(M) algebra, which is generated by parallel transports along flows of vector fields and translation operators on an underlying configuration space of connections, and involves a semi-final spectral triple with an infinite-dimensional Bott-Dirac operator. Previously we have proven that the square of the Bott-Dirac operator gives the free Hamilton operator of a Yang-Mills theory coupled to a fermionic sector in a flat and local limit. In this paper we show that the Hilbert space representation, that forms the backbone in this construction, can be extended to include many-particle states.