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arXiv · 1403.7263

A $P$-Adic Spectral Triple

Slawomir Klimek·Matt McBride·Sumedha Rathnayake
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Abstract

We construct a spectral triple for the C$^*$-algebra of continuous functions on the space of $p$-adic integers by using a rooted tree obtained from coarse-grained approximation of the space, and the forward derivative on the tree. Additionally, we verify that our spectral triple satisfies the properties of a compact spectral metric space, and we show that the metric on the space of $p$-adic integers induced by the spectral triple is equivalent to the usual $p$-adic metric.

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Slawomir Klimek, Matt McBride, Sumedha Rathnayake. 2014-03-31. A $P$-Adic Spectral Triple. https://doi.org/10.1063/1.4900923

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