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arXiv · 1502.05383

Matrix geometries and fuzzy spaces as finite spectral triples

John W. Barrett
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Abstract

A class of real spectral triples that are similar in structure to a Riemannian manifold but have a finite-dimensional Hilbert space is defined and investigated, determining a general form for the Dirac operator. Examples include fuzzy spaces defined as real spectral triples. Fuzzy 2-spheres are investigated in detail, and it is shown that the fuzzy analogues correspond to two spinor fields on the commutative sphere. In some cases it is necessary to add a mass mixing matrix to the commutative Dirac operator to get a precise agreement for the eigenvalues.

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John W. Barrett. 2015-02-18. Matrix geometries and fuzzy spaces as finite spectral triples. https://doi.org/10.1063/1.4927224

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