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Matrix geometries and fuzzy spaces as finite spectral triples
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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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Fuzzy Geometries with an Internal Space
Product of noncommutative spectral triple with 2D internal space yields charged fermion model whose fluctuations produce gauge fields, geometry changes, charge-dependent derivative, and novel induced bosonic terms.
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