What Are Observables in Hamiltonian Einstein-Maxwell Theory?
What Are Observables in Hamiltonian Einstein-Maxwell Theory?
复制标题
哈密顿爱因斯坦-麦克斯韦理论中的可观测量是什么？
DOI：
10.1007/s10701-019-00284-w
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发表时间：
2019
影响因子：
1.5
通讯作者：
Pitts, J. Brian
中科院分区：
文献类型：
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作者：
Pitts, J. Brian
爱因斯坦-麦克斯韦哈密顿理论中缺少变化吗？给定观测量的最常见定义（具有弱消失泊松括号和每个第一类约束），观测量是运动的常数和非局部的。不幸的是，这个定义也意味着有规范自由的大质量电磁学（“Stueckelberg”）的可观测量量与没有规范自由的大质量电磁学（“Proca”）的可观测量量是不等价的。另一种Pons-Salisbury-Sundermeyer的观测量定义，旨在实现哈密顿-拉格朗日等价，使用规范生成元G，一个第一类约束的调谐和，而不是每个第一类约束单独，并意味着等效的大质量电磁学的等效观测量。对于广义相对论，G生成解的四维李导数。李导数比较了不同坐标系中具有相同坐标值的不同时空点，例如夏季时间凌晨1点与标准时间凌晨1点，因此消失的李导数意味着常数而不是协方差。等价的大质量引力公式需要等价的观测量，这就证实了G必须生成观测量的四维李导数（不是0）。这些独立的结果表明，观测量在内部规范对称下是不变的，但在外部规范对称下是协变的，但这种分叉的定义能适用于爱因斯坦-麦克斯韦理论等混合理论吗？脑桥、索尔兹伯里和谢普利研究了爱因斯坦-杨-米尔斯的G。对于Einstein-Maxwell，和在电磁规范变换下是不变的，在四维坐标变换下是协变的（由Lie导数改变）。使用分叉的定义，这些量被视为可观测量，正如人们在非哈密顿基础上所期望的那样。
Is change missing in Hamiltonian Einstein–Maxwell theory? Given the most common definition of observables (having weakly vanishing Poisson bracket with each first-class constraint), observables are constants of the motion and nonlocal. Unfortunately this definition also implies that the observables for massive electromagnetism with gauge freedom (‘Stueckelberg’) are inequivalent to those of massive electromagnetism without gauge freedom (‘Proca’). The alternative Pons–Salisbury–Sundermeyer definition of observables, aiming for Hamiltonian–Lagrangian equivalence, uses the gauge generatorG, a tuned sum of first-class constraints, rather than each first-class constraint separately, and implies equivalent observables for equivalent massive electromagnetisms. For General Relativity,Ggenerates 4-dimensional Lie derivatives for solutions. The Lie derivative compares different space-time points with the same coordinate value in different coordinate systems, like 1 a.m. summer time versus 1 a.m. standard time, so a vanishing Lie derivative implies constancy rather than covariance. Requiring equivalent observables for equivalent formulations of massive gravity confirms thatGmust generate the 4-dimensional Lie derivative (not 0) for observables. These separate results indicate that observables are invariant under internal gauge symmetries but covariant under external gauge symmetries, but can this bifurcated definition work for mixed theories such as Einstein–Maxwell theory? Pons, Salisbury and Shepley have studiedGfor Einstein–Yang–Mills. For Einstein–Maxwell, bothandare invariant under electromagnetic gauge transformations and covariant (changing by a Lie derivative) under 4-dimensional coordinate transformations. Using the bifurcated definition, these quantities count as observables, as one would expect on non-Hamiltonian grounds.