规范约束超选
Superselection from canonical constraints
摘要：
量子系综和经典系综的演化可以通过位形空间上的概率密度P、其正则共轭S和系综哈密顿量H[P，S]来描述。当然，对于量子系综，这种演化等价于波函数的薛定谔方程，它是线性的。然而，对正则场P和S的非常简单的约束对应于对波函数的_非线性_约束。这样的限制作用于阻止波函数的某些叠加被实现，导致超选择型规则。给出了导致能量、自旋方向和“经典性”的超选择的例子。运动方程的规范公式，在概率密度和共轭方面，提供了一种通用的语言，用于描述连续和离散配置空间上的经典和量子系综，并在附录中简要回顾。
英文摘要：
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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