Michael J W Hall 2004 J. Phys. A: Math. Gen. 37 7799 doi:10.1088/0305-4470/37/31/011
Superselection from canonical constraints
Michael J W Hall
Show affiliationsThe evolution of both quantum and classical ensembles may be described via the probability density P on configuration space, its canonical conjugate S, and an ensemble Hamiltonian ![\skew3\tilde{H}[P,S]](http://ej.iop.org/images/0305-4470/37/31/011/jpa179505ieqn1.gif)
. For quantum ensembles this evolution is, of course, equivalent to the Schrödinger equation for the wavefunction, which is linear. However, quite simple constraints on the canonical fields P and S correspond to nonlinear constraints on the wavefunction. Such constraints act to prevent certain superpositions of wavefunctions from being realized, leading to superselection-type rules. Examples leading to superselection for energy, spin direction and 'classicality' are given. The canonical formulation of the equations of motion, in terms of a probability density and its conjugate, provides a universal language for describing classical and quantum ensembles on both continuous and discrete configuration spaces, and is briefly reviewed in an appendix.
- PACS
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03.65.Ge Solutions of wave equations: bound states
03.65.Ta Foundations of quantum mechanics; measurement theory
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- Dates
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Issue 31 (6 August 2004)
Received 21 April 2004, in final form 1 June 2004
Published 21 July 2004
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Superselection from canonical constraints
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