A Hardy-type inequality and some spectral characterizations for the Dirac-Coulomb operator

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61389005%3A_____%2F20%3A00522522" target="_blank" >RIV/61389005:_____/20:00522522 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1007/s13163-019-00311-4" target="_blank" >https://doi.org/10.1007/s13163-019-00311-4</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s13163-019-00311-4" target="_blank" >10.1007/s13163-019-00311-4</a>

Result language
angličtina
Original language name
A Hardy-type inequality and some spectral characterizations for the Dirac-Coulomb operator
Original language description
We prove a sharp Hardy-type inequality for the Dirac operator. We exploit this inequality to obtain spectral properties of the Dirac operator perturbed with Hermitian matrix-valued potentials V of Coulomb type: we characterise its eigenvalues in terms of the Birman-Schwinger principle and we bound its discrete spectrum from below, showing that the ground-state energy is reached if and only if V verifies some rigidity conditions. In the particular case of an electrostatic potential, these imply that V is the Coulomb potential.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GA17-01706S" target="_blank" >GA17-01706S: Mathematical-Physics Models of Novel Materials</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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