精化代数量子化中的约束重标度：动量约束
Constraint rescaling in refined algebraic quantisation: momentum constraint
摘要：
我们调查精细代数量子化内的一个家庭的经典等价的约束哈密顿系统是相互关联的重新缩放的动量型约束。量子约束是由一个操纵地图，这是由组平均的动机，但有一个分辨率比什么可以剥离的平均积分的正式分歧的贡献。三种情况出现，取决于渐近的重标度函数：（i）量化是等效的身份缩放;（ii）量化失败，由于不存在的自伴扩展的约束算子;（iii）量化模糊性由约束算子的自伴扩展引起，而这种纯粹量子力学的模糊性的解决决定了物理希尔伯特空间的超选择结构。展望推广的分析系统与几个约束条件进行了讨论。
英文摘要：
We investigate refined algebraic quantisation within a family of classically equivalent constrained Hamiltonian systems that are related to each other by rescaling a momentum-type constraint. The quantum constraint is implemented by a rigging map that is motivated by group averaging but has a resolution finer than what can be peeled off from the formally divergent contributions to the averaging integral. Three cases emerge, depending on the asymptotics of the rescaling function: (i) quantisation is equivalent to that with identity scaling; (ii) quantisation fails, owing to nonexistence of self-adjoint extensions of the constraint operator; (iii) a quantisation ambiguity arises from the self-adjoint extension of the constraint operator, and the resolution of this purely quantum mechanical ambiguity determines the superselection structure of the physical Hilbert space. Prospects of generalising the analysis to systems with several constraints are discussed.
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