TY - JOUR

T1 - Superselection from canonical constraints

AU - Hall, Michael J.W.

PY - 2004/8/6

Y1 - 2004/8/6

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=4043090697&partnerID=8YFLogxK

U2 - 10.1088/0305-4470/37/31/011

DO - 10.1088/0305-4470/37/31/011

M3 - Article

SN - 0305-4470

VL - 37

SP - 7799

EP - 7811

JO - Journal of Physics A: Mathematical and General

JF - Journal of Physics A: Mathematical and General

IS - 31

ER -