# Understanding truncated non-commutative geometries through computer simulations

@article{Glaser2019UnderstandingTN, title={Understanding truncated non-commutative geometries through computer simulations}, author={L. Glaser and Abel B. Stern}, journal={arXiv: Mathematical Physics}, year={2019} }

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 places on a truncated Dirac operator. We find a bounded perturbation of the Dirac…

## 9 Citations

Reconstructing manifolds from truncations of spectral triples

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Abstract We explore the geometric implications of introducing a spectral cut-off on compact Riemannian manifolds. This is naturally phrased in the framework of non-commutative geometry, where we work…

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We analyze the perturbative quantization of the spectral action in noncommutative geometry and establish its one-loop renormalizability as a gauge theory. Our result is based on the perturbative…

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We explore the geometric implications of introducing a spectral cut-off on Riemannian manifolds. This is naturally phrased in the framework of non-commutative geometry, where we work with spectral…

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It is well known that “bad” quotient spaces (typically: non-Hausdorff) can be studied by associating to them the groupoid C*-algebra of an equivalence relation, that in the “nice” cases is Morita…

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We study the convergence aspects of the metric on spectral truncations of geometry. We find general conditions on sequences of operator system spectral triples that allows one to prove a result on…

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Random noncommutative geometry can be seen as a Euclidean path-integral approach to the quantization of the theory defined by the Spectral Action in noncommutative geometry (NCG). With the aim of…

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In this paper we extend the traditional framework of noncommutative geometry in order to deal with spectral truncations of geometric spaces (i.e. imposing an ultraviolet cutoff in momentum space) and…

Computing the spectral action for fuzzy geometries: from random noncommutatative geometry to bi-tracial multimatrix models

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A fuzzy geometry is a certain type of spectral triple whose Dirac operator crucially turns out to be a finite matrix. This notion was introduced in [J. Barrett, J. Math. Phys. 56, 082301 (2015)] and…

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