Geometric properties of the magnetic Laplacian on the Euclidean 4-space

Journal Article · Wed Dec 15 04:00:00 EST 2010 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.3520526· OSTI ID:21501233

Kazmierowski, Dominique ^[1]; Zinoun, Azzouz ^[2]; Intissar, Ahmed ^[3]

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1. Universite Lille I - Sciences et Technologies, 59655 Villeneuve d'Ascq Cedex (France)
2. Laboratoire de Physique des Lasers, Atomes et Molecules, Unite Mixte de Recherche de l'Universite de Lille 1 et du CNRS - UMR 8523, Universite Lille I - Sciences et Technologies, 59655 Villeneuve d'Ascq Cedex (France)
3. Departement de Mathematiques, Faculte des Sciences de Rabat, BP 1014 (Morocco)

When the four-dimensional Euclidean space is endowed with a covariant derivative that is either self-dual or antiself-dual and of constant curvature, the corresponding magnetic Laplacian is closely related to the sub-Laplacian of the quaternionic Heisenberg group. Some geometric properties of this operator are studied. In particular, it is proved that there exists a canonical orthogonal complex structure which provides a factorization in the sense of Schroedinger.

• OSTI ID: 21501233
• Journal Information: Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 12 Vol. 51; ISSN JMAPAQ; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

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FOUR-DIMENSIONAL CALCULATIONS
GEOMETRY
HARMONIC OSCILLATORS
HEISENBERG MODEL
LAPLACIAN
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