Superselection from canonical constraints

Michael J.W. Hall*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

16 Citations (Scopus)


The 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 H̃[P, S]. 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.

Original languageEnglish
Pages (from-to)7799-7811
Number of pages13
JournalJournal of Physics A: Mathematical and General
Issue number31
Publication statusPublished - 6 Aug 2004


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