Matrix geometries and fuzzy spaces as finite spectral triples - INSPIRE

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Matrix geometries and fuzzy spaces as finite spectral triples

John W. Barrett
(
- Nottingham U.
)

Feb 18, 2015

39 pages

Published in:

J.Math.Phys. 56 (2015) 8, 082301

Published: Aug 3, 2015

e-Print:

1502.05383 [math-ph]

DOI:

10.1063/1.4927224

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Abstract: (AIP)

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.

Note:

39 pages, final version

space: fuzzy
operator: Dirac
sphere: fuzzy
field theory: spinor
spectral triple
Hilbert space
geometry
algebra: Lie
space: Riemann

References(22)

Figures(0)

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