The relativistic spherical δ-shell interaction in R3: Spectrum and approximation

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URI: https://hdl.handle.net/10902/29138
ISSN: 0022-2488
ISSN: 1089-7658
ISSN: 1527-2427
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Autoría
Mas Blesa, Albert; Pizzichillo, FabioAutoridad Unican
Fecha
2017-08-30
Derechos
© American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. The following article appeared in Albert Mas, Fabio Pizzichillo; The relativistic spherical δ-shell interaction in R3⁠: Spectrum and approximation. J. Math. Phys. 1 August 2017; 58 (8): 082102 and may be found at https://doi.org/10.1063/1.5000381
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Journal of Mathematical Physics, 2017, 58(8), 082102
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American Institute of Physics
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Palabras clave
Dirac operator
Self-adjoint extension
Spherical δ-shell interaction
Singular integral
Approximation by scaled regular potentials
Resumen/Abstract
This note revolves on the free Dirac operator in R3 and its δ-shell interaction with electrostatic potentials supported on a sphere. On one hand, we characterize the eigenstates of those couplings by finding sharp constants and minimizers of some precise inequalities related to an uncertainty principle. On the other hand, we prove that the domains given by Dittrich et al. [J. Math. Phys. 30(12), 2875-2882 (1989)] and by Arrizabalaga et al. [J. Math. Pures Appl. 102(4), 617-639 (2014)] for the realization of an electrostatic spherical shell interaction coincide. Finally, we explore the spectral relation between the shell interaction and its approximation by short range potentials with shrinking support, improving previous results in the spherical case.
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