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dc.contributor.authorKarasev, MV
dc.contributor.authorOsborn, TA
dc.date.accessioned2007-10-10T18:36:12Z
dc.date.available2007-10-10T18:36:12Z
dc.date.issued2006-07-31
dc.identifier.citation0008-4204; CAN J PHYS, JUN-JUL 2006, vol. 84, no. 39240, p.551 to 556.en
dc.identifier.urihttp://hdl.handle.net/1993/2933
dc.description.abstractWe demonstrate that Weyl's pioneering idea (1918) to intertwine metric and magnetic fields into a single joint connection can be naturally realized, on the phase space level, by the gauge-invariant quantization of the cotangent bundle with magnetic symplectic form. Quantization, for systems over a noncompact Riemannian configuration manifold, may be achieved by the introduction of a magneto-metric analog of the Stratonovich quantizer - a family of invertible, selfadjoint operators representing quantum delta functions. Based on the quantizer, we construct a generalized Wigner transform that maps Hilbert-Schmidt operators into L-2 phase-space functions. The algebraic properties of the quantizer allow one to extract a family of symplectic reflections, which are then used to (i) derive a simple, explicit, and geometrically invariant formula for the noncommutative product of functions on phase space, and (ii) construct a magneto-metric connection on phase space. The classical limit of this product is given by the usual multiplication of functions (zeroth-order term), the magnetic Poisson bracket (first-order term), and by the magneto-metric connection (second-order term).en
dc.format.extent103531 bytes
dc.format.mimetypeapplication/pdf
dc.language.isoengen_US
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dc.rightsinfo:eu-repo/semantics/openAccess
dc.subjectRiemannian manifoldsen
dc.subjectmagnetic quantizationen
dc.titleMagnetic quantization over Riemannian manifoldsen
dc.typejournal articleen_US
dc.typeinfo:eu-repo/semantics/article
dc.statusPeer revieweden
dc.identifier.doihttp://dx.doi.org/10.1139/p06-027


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