从类时Killing矢量场的缺失看哈密顿广义相对论的变化
Change in Hamiltonian General Relativity from the Lack of a Time-like Killing Vector Field
摘要：
在广义相对论的哈密顿形式中，变化似乎是缺失的，仅仅是渐近地定义的，或者充其量是模糊的，因为哈密顿量是第一类约束和边界项的总和，因此被认为会产生规范变换。注意Rosenfeld，Anderson，Bergmann，Castellani等人的规范生成器G，第一类约束的特别调整的总和，便于看到，一个孤立的第一类约束实际上产生的不是规范变换，但在电磁（改变E）或GR坏的物理变化。变化破坏拉格朗日约束的物理相关的速度，而不是辅助正则动量。虽然Maudlin为GR的变化辩护，但G。E.摩尔拒绝了怀疑论，仍然有必要展示论证中的技术缺陷。坚持哈密顿拉格朗日等价，一个由Mukunda，Castellani，Sugano，Pons，Salisbury，Shepley和Sundermeyer等人强调的主题，是关键。假设客观变化是不可消除的时间依赖性，只要不存在满足Killing方程的类时矢量场，真空GR就有变化。为了方便起见，抛开GR的空间依赖性，我们发现，只有当不存在类时Killing矢量时，Hamilton方程的时间演化才是真实的变化。因此，变化是真实的和局部的，即使在汉密尔顿形式主义中也是如此。这里的考虑解决了厄尔曼-莫德林的僵局：汉密尔顿的形式主义是有帮助的，而且经过适当的改革，它不会对变化产生荒谬的后果。因此，经典的时间问题得到解决，除了可观测量的问题，其中的解决方案概述。然而，由于量子约束强加的问题，时间的量子问题不会自动解决。
英文摘要：
In General Relativity in Hamiltonian form, change has seemed to be missing, defined only asymptotically, or otherwise obscured at best, because the Hamiltonian is a sum of first-class constraints and a boundary term and thus supposedly generates gauge transformations. Attention to the gauge generator G of Rosenfeld, Anderson, Bergmann, Castellani et al., a specially tuned sum of first-class constraints, facilitates seeing that a solitary first-class constraint in fact generates not a gauge transformation, but a bad physical change in electromagnetism (changing E) or GR. The change spoils the Lagrangian constraints in terms of the physically relevant velocities rather than auxiliary canonical momenta. While Maudlin has defended change in GR much as G. E. Moore resisted skepticism, there remains a need to exhibit the technical flaws in the argument. Insistence on Hamiltonian-Lagrangian equivalence, a theme emphasized by Mukunda, Castellani, Sugano, Pons, Salisbury, Shepley and Sundermeyer among others, holds the key. Taking objective change to be ineliminable time dependence, there is change in vacuum GR just in case there is no time-like vector field satisfying Killing's equation. Throwing away the spatial dependence of GR for convenience, one finds that the time evolution from Hamilton's equations is real change just when there is no time-like Killing vector. Hence change is real and local even in the Hamiltonian formalism. The considerations here resolve the Earman-Maudlin standoff: the Hamiltonian formalism is helpful, and, suitably reformed, it does not have absurd consequences for change. Hence the classical problem of time is resolved, apart from the issue of observables, for which the solution is outlined. The quantum problem of time, however, is not automatically resolved due to issues of quantum constraint imposition.
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