Classical dynamics as constrained quantum dynamics

doi:10.1088/0305-4470/36/6/312

Classical dynamics as constrained quantum dynamics

Stephen D Bartlett et al 2003 J. Phys. A: Math. Gen. 36 1683-1704 doi: 10.1088/0305-4470/36/6/312

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Stephen D Bartlett^1,2 and David J Rowe²
¹ Department of Physics, University of Toronto, Toronto, Ontario M5S 1A7, Canada
² Department of Physics, Macquarie University, Sydney, New South Wales 2109, Australia

Abstract. We show that the classical mechanics of an algebraic model are implied by its quantizations. An algebraic model is defined, and the corresponding classical and quantum realizations are given in terms of a spectrum generating algebra. Classical equations of motion are then obtained by constraining the quantal dynamics of an algebraic model to an appropriate coherent state manifold. For the cases where the coherent state manifold is not symplectic, it is shown that there exist natural projections onto classical phase spaces. These results are illustrated with the extended example of an asymmetric top.

PACS numbers: 03.65.Fd, 03.65.Sq

Print publication: Issue 6 (14 February 2003)
Received 21 November 2002
Published 29 January 2003

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