The semiclassical structure of low-energy states in the presence of a magnetic field

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dc.creatorBorthwick, David
dc.creatorUribe, Alejandro
dc.date2004-12-11
dc.date.accessioned2026-07-07T05:15:13Z
dc.date.available2026-07-07T05:15:13Z
dc.descriptionWe consider a compact Riemannian manifold with a Hermitian line bundle whose curvature is non-degenerate. The Laplacian acting on high tensor powers (the semiclassical regime) of the bundle exhibits a cluster of low-energy states. We demonstrate that the orthogonal projectors onto these states are the Fourier components of an operator with the structure of the Szegö projector, i.e. a Fourier integral operator of Hermite type. This result yields semiclassical asymptotics for the low-energy eigenstates.
dc.description15 pages
dc.identifierhttps://arxiv.org/abs/math/0412223
dc.identifierhttp://arxiv.org/abs/math/0412223
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/73557
dc.subjectSpectral Theory
dc.subjectDifferential Geometry
dc.subject58J50
dc.titleThe semiclassical structure of low-energy states in the presence of a magnetic field
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