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.
Relativistic Hardy Inequalities in Magnetic Fields / Fanelli, Luca; Luis, Vega; Nicola, Visciglia. - In: JOURNAL OF STATISTICAL PHYSICS. - ISSN 0022-4715. - STAMPA. - 154:3(2014), pp. 866-876. [10.1007/s10955-014-0915-0]
Relativistic Hardy Inequalities in Magnetic Fields
FANELLI, Luca;
2014
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
