Finite spectral triples for the fuzzy torus
Quantum Algebra
2024-10-31 v2 General Relativity and Quantum Cosmology
High Energy Physics - Theory
Mathematical Physics
math.MP
Abstract
Finite real spectral triples are defined to characterise the non-commutative geometry of a fuzzy torus. The geometries are the non-commutative analogues of flat tori with moduli determined by integer parameters. Each of these geometries has four different Dirac operators, corresponding to the four unique spin structures on a torus. The spectrum of the Dirac operator is calculated. It is given by replacing integers with their quantum integer analogues in the spectrum of the corresponding commutative torus.
Keywords
Cite
@article{arxiv.1908.06796,
title = {Finite spectral triples for the fuzzy torus},
author = {John W. Barrett and James Gaunt},
journal= {arXiv preprint arXiv:1908.06796},
year = {2024}
}
Comments
53 pages, 6 figures. v2: more detail on the square of the Dirac operator; some eigenvalue plots removed. Journal accepted MS