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arXiv · 1908.06796

Finite spectral triples for the fuzzy torus

John W. Barrett·James Gaunt
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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.

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John W. Barrett, James Gaunt. 2019-08-19. Finite spectral triples for the fuzzy torus. https://arxiv.org/abs/1908.06796

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