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Springer Verlag, Journal of Statistical Physics, 3(154), p. 866-876

DOI: 10.1007/s10955-014-0915-0

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Relativistic Hardy Inequalities in Magnetic Fields

Journal article published in 2013 by Luca Fanelli, Luis Vega ORCID, Nicola Visciglia
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This paper is available in a repository.

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Abstract

We deal with Dirac operators with external homogeneous magnetic fields. Hardy-type inequalities related to these operators are investigated: for a suitable class of transversal magnetic fields, we prove a Hardy inequality with the same best constant as in the free case. This leaves naturally open an interesting question whether there exist magnetic fields for which a Hardy inequality with a better constant than the usual one, in connection with the well known diamagnetic phenomenon arising in non-relativistic models.