Does noncommutative geometry encompass lattice gauge theory?
Meinulf Goeckeler, Thomas Schuecker
TL;DR
This paper investigates whether noncommutative geometry, specifically Connes' spectral triples, can be used to formulate lattice gauge theories, and concludes that it currently cannot.
Contribution
The paper demonstrates the limitations of Connes' spectral triples in representing lattice gauge theories, highlighting a gap in the application of noncommutative geometry.
Findings
Spectral triples cannot currently formulate lattice gauge theories
Identifies a fundamental gap in noncommutative geometric approaches
Suggests need for new frameworks or extensions
Abstract
We are unable to formulate lattice gauge theories in the framework of Connes' spectral triples.
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