Show simple item record Karasev, MV Osborn, TA 2007-10-10T18:36:12Z 2007-10-10T18:36:12Z 2006-07-31
dc.identifier.citation 0008-4204; CAN J PHYS, JUN-JUL 2006, vol. 84, no. 39240, p.551 to 556. en
dc.description.abstract We 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
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dc.language.iso en_US
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dc.subject Riemannian manifolds en
dc.subject magnetic quantization en
dc.title Magnetic quantization over Riemannian manifolds en
dc.status Peer reviewed en

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