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arXiv · 2204.00965

The Calder\'on problem for the fractional Dirac operator

Hadrian Quan·Gunther Uhlmann
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Abstract

We show that knowledge of the source-to-solution map for the fractional Dirac operator acting over sections of a Hermitian vector bundle over a smooth closed connencted Riemannian manifold of dimension $m\geq 2$ determines uniquely the smooth structure, Riemannian metric, Hermitian bundle and connection, and its Clifford modulo up to a isometry. We also mention several potential applications in physics and other fields.

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Hadrian Quan, Gunther Uhlmann. 2022-04-03. The Calder\'on problem for the fractional Dirac operator. https://doi.org/10.4310/mrl.240904213421

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