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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.identifier.citation 0008-4204; CAN J PHYS, JUN-JUL 2006, vol. 84, no. 39240, p.551 to 556. en
dc.identifier.uri http://hdl.handle.net/1993/2933
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.language.iso en_US
dc.rights No part of the NRC Research Press electronic journals may be reproduced, stored, or transmitted in any form or by any means, without the written permission of the publisher, except as stated below. Under the Canadian Copyright Act, individuals may download or print single copies of articles for personal research or study. Any person may reproduce short excerpts from articles in the journals for any purpose that respects the moral rights of authors, provided that the source is fully acknowledged. As a courtesy, the consent of authors of such material should be obtained directly from the author. Authorization to reproduce items for other than personal research or study, as stated above, may be obtained via Access © upon payment of the copyright fee of $10.00 per copy. NRC Research Press also extends certain additional rights to authors. The above rights do not extend to copying or reproduction for general distribution, for advertising or promotional purposes, for creating new collective works, or for resale. For such copying or reproduction, arrangements must be made with NRC Research Press. en
dc.rights info:eu-repo/semantics/restrictedAccess
dc.subject Riemannian manifolds en
dc.subject magnetic quantization en
dc.title Magnetic quantization over Riemannian manifolds en
dc.status Peer reviewed en
dc.identifier.doi http://dx.doi.org/10.1139/p06-027


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