Dirac operator associated to a quantum metric

  • Shahn Majid

    Queen Mary University of London, UK
Dirac operator associated to a quantum metric cover
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Abstract

We construct a canonical geometrically realised Connes spectral triple or ‘Dirac operator’ from the data of a quantum metric and a bimodule connection on , at the pre-Hilbert space level. Here is a possibly noncommutative coordinate algebra, a bimodule of -forms and the spinor bundle is . When applied to graphs or lattices, we essentially recover a previously proposed Dirac operator but now as a geometrically realised spectral triple. We also apply the construction to the fuzzy sphere and to matrices with their standard quantum Riemannian geometries. We propose how can be extended to an external bundle with bimodule connection.

Cite this article

Shahn Majid, Dirac operator associated to a quantum metric. J. Noncommut. Geom. (2024), published online first

DOI 10.4171/JNCG/570