arXiv 1609.048122016-09gr-qchep-thphysics.hist-ph

等价理论重新定义哈密顿量以体现广义相对论的变化

Equivalent Theories Redefine Hamiltonian Observables to Exhibit Change in General Relativity

J. Brian Pitts

备注：: Published in Classical and Quantum Gravity. A related CQG+ article is on the way
发表信息：: Classical and Quantum Gravity 34 (2017) 055008
DOI：: 10.1088/1361-6382/aa5ce8

摘要：

变化和局部空间变化在典型的广义相对论的观测量中是缺失的，这是时间问题的一部分。定义可以用等价的公式来检验，非规范和规范，因为它们必须有等价的可观测量，并且在非规范公式中一切都是可观测的。从非规范公式中取一个可观测量，并在规范公式中找到等价物，要求等价物是一个可观测的、约束性的定义。对于大质量光子，de Broglie-Proca非规范形式的可观测量A μ等价于Stueckelberg-Utiyama规范形式的量A μ + \partial_μ μ。因此，观测量必须有0泊松括号不是与每个第一类约束，但与罗森伯格-安德森-伯格曼-卡斯特拉尼规范生成器G，一个调谐的和第一类约束，符合庞斯-索尔兹伯里-桑德迈尔定义的观测量。外部规范对称性的定义可以用质量引力来检验，其中可以通过用时钟场X ^A参数化来安装规范自由度。非规范可观测g ^{μ ν}具有规范等价物X ^A，_μ g ^{μ ν} X ^B，_ν。X ^A，_μ g ^{μ ν} X ^B，_ν对G的泊松括号不是0而是一个李导数。这个非零的泊松括号细化和系统化库查尔的建议放松0泊松括号条件与哈密顿约束。因此，可观测量相对于外部规范对称性需要协变性，而不是不变性。大质量引力的拉格朗日量和哈密顿量是广义相对论+ λ +4标量的拉格朗日量和哈密顿量，因此相同的可观测量定义也适用于广义相对论。局部字段（如g_{μν}）是可观察的。因此，可观察到的变化。等价理论要求等价的观测量也恢复了哈密顿-拉格朗日等价性。

英文摘要：

Change and local spatial variation are missing in canonical General Relativity's observables as usually defined, part of the problem of time. Definitions can be tested using equivalent formulations, non-gauge and gauge, because they must have equivalent observables and everything is observable in the non-gauge formulation. Taking an observable from the non-gauge formulation and finding the equivalent in the gauge formulation, one requires that the equivalent be an observable, constraining definitions. For massive photons, the de Broglie-Proca non-gauge formulation observable A_μ is equivalent to the Stueckelberg-Utiyama gauge formulation quantity A_μ+\partial_μ ϕ. Thus observables must have 0 Poisson bracket not with each first-class constraint, but with the Rosenfeld-Anderson-Bergmann-Castellani gauge generator G, a tuned sum of first-class constraints, in accord with the Pons-Salisbury-Sundermeyer definition of observables. The definition for external gauge symmetries can be tested using massive gravity, where one can install gauge freedom by parametrization with clock fields X^A. The non-gauge observable g^{μν} has the gauge equivalent X^A,_μ g^{μν} X^B,_ν. The Poisson bracket of X^A,_μ g^{μν} X^B,_ν with G turns out to be not 0 but a Lie derivative. This non-zero Poisson bracket refines and systematizes Kuchar's proposal to relax the 0 Poisson bracket condition with the Hamiltonian constraint. Thus observables need covariance, not invariance, in relation to external gauge symmetries. The Lagrangian and Hamiltonian for massive gravity are those of General Relativity + Lambda + 4 scalars, so the same definition of observables applies to General Relativity. Local fields such as g_{μν} are observables. Thus observables change. Requiring equivalent observables for equivalent theories also recovers Hamiltonian-Lagrangian equivalence.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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