Dirac Operators on Configuration Spaces and Yang-Mills Quantum Field Theory
High Energy Physics - Theory
2024-10-18 v3 General Relativity and Quantum Cosmology
Mathematical Physics
math.MP
Abstract
In this paper we discuss a connection between Dirac operators on configuration spaces and Yang-Mills quantum field theory. We first show that the Hamilton operators of the self-dual and anti-self-dual sectors of a Yang-Mills quantum field theory emerge from unitary transformations of a Dirac equation formulated on a configuration space of gauge connections. Secondly, we formulate a Bott-Dirac operator on the configuration space and demonstrate how the Hamilton operator of a Yang-Mills quantum field theory coupled to a fermionic sector emerges from its square. Finally, we discuss a spectral invariant that emerges in this framework.
Cite
@article{arxiv.2410.03699,
title = {Dirac Operators on Configuration Spaces and Yang-Mills Quantum Field Theory},
author = {Johannes Aastrup and Jesper M. Grimstrup},
journal= {arXiv preprint arXiv:2410.03699},
year = {2024}
}
Comments
10 pages