A p-adic spectral triple
Abstract
We construct a spectral triple for the C*-algebra of continuous functions on the space of p-adic integers. On the technical level we utilize a weighted rooted tree obtained from a coarse grained approximation of the space combined with the forward derivative D on the tree. Our spectral triple satisfies the properties of a compact spectral metric space and the metric on the space of p-adic integers induced by the spectral triple is equivalent to the usual p-adic metric. Furthermore, we show that the spectrum of the operator D*D is closely related to the roots of a certain q-hypergeometric function and discuss the analytic continuation of the zeta function associated with D*D.
Degree
Ph.D.
Advisors
Klimek, Purdue University.
Subject Area
Mathematics
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