Spectral asymptotics of the Dirac operator in a thin shell

Vladimir Lotoreichik; Thomas Ourmières-Bonafos

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arXiv · 2307.09033

Spectral asymptotics of the Dirac operator in a thin shell

Vladimir Lotoreichik·Thomas Ourmières-Bonafos

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Abstract

We investigate the spectrum of the Dirac operator with infinite mass boundary conditions posed in a tubular neighborhood of a smooth compact hypersurface in $\mathbb{R}^n$ without boundary. We prove that when the tubular neighborhood shrinks to the hypersurface, the asymptotic behavior of the eigenvalues is driven by a Schr\"odinger operator involving electric and Yang-Mills potentials, both of geometric nature.

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BibTeX RIS

Vladimir Lotoreichik, Thomas Ourmières-Bonafos. 2023-07-18. Spectral asymptotics of the Dirac operator in a thin shell. https://arxiv.org/abs/2307.09033

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