Magnetic quantization over Riemannian manifolds
| dc.contributor.author | Karasev, MV | |
| dc.contributor.author | Osborn, TA | |
| dc.date.accessioned | 2007-10-10T18:36:12Z | |
| dc.date.available | 2007-10-10T18:36:12Z | |
| dc.date.issued | 2006-07-31 | |
| 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 |
| dc.format.extent | 103531 bytes | |
| dc.format.mimetype | application/pdf | |
| dc.identifier.citation | 0008-4204; CAN J PHYS, JUN-JUL 2006, vol. 84, no. 39240, p.551 to 556. | en |
| dc.identifier.doi | http://dx.doi.org/10.1139/p06-027 | |
| dc.identifier.uri | http://hdl.handle.net/1993/2933 | |
| dc.language.iso | eng | en_US |
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| dc.rights | open access | en_US |
| dc.status | Peer reviewed | en |
| dc.subject | Riemannian manifolds | en |
| dc.subject | magnetic quantization | en |
| dc.title | Magnetic quantization over Riemannian manifolds | en |
| dc.type | journal article | en_US |