Superselection from canonical constraints

Details Superselection from canonical constraints Superselection from canonical constraints

2004-04-21

arxiv.org/abs/quant-ph/0404123v2

J.Phys. A37 (2004) 7799-7812

Physics

Quantum Physics

MiKTex 2.3, no figures, minor clarifications, to appear in J. Phys. A

Scientific paper

10.1088/0305-4470/37/31/011

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 H[P,S]. For quantum ensembles this evolution is, of course, equivalent to the Schroedinger 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 realised, 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.

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