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arXiv · 1909.08054

Understanding truncated non-commutative geometries through computer simulations

Lisa Glaser·Abel Stern
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Abstract

When aiming to apply mathematical results of non-commutative geometry to physical problems the question arises how they translate to a context in which only a part of the spectrum is known. In this article we aim to detect when a finite-dimensional triple is the truncation of the Dirac spectral triple of a spin manifold. To that end, we numerically investigate the restriction that the higher Heisenberg equation [A. H. Chamseddine, A. Connes, and V. Mukhanov, Journal of High Energy Physics, 98 (2014)] places on a truncated Dirac operator. We find a bounded perturbation of the Dirac operator on the Riemann sphere that induces the same Chern class.

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Lisa Glaser, Abel Stern. 2020-03-17. Understanding truncated non-commutative geometries through computer simulations. https://doi.org/10.1063/1.5131864

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