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Finite spectral triples for the fuzzy torus (1908.06796v2)
Published 19 Aug 2019 in math.QA, gr-qc, hep-th, math-ph, and 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.
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