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 -