Superselection from canonical constraints

Abstract

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.

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

References in corpus (4)

• Continuous Quantum Measurement and the Emergence of Classical Chaos
• Schrodinger equation from an exact uncertainty principle
• Bosonic field equations from an exact uncertainty principle
• Modal dynamics for positive operator measures

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