论文标题
彼得·伯格曼（Peter Bergmann
Peter Bergmann on Observables in Hamiltonian General Relativity: A Historical-Critical Investigation
论文作者
论文摘要
自1950年代以来，观察到的问题及其所谓的缺乏变化在哈密顿量子引力中显着。本文考虑了发明了观察力的彼得·伯格曼（Peter Bergmann）的思想，考虑了关于观察力的各种观念。最初，他要求受约束的哈密顿形式主义在数学上等同于拉格朗日，但1953年，伯格曼和席勒（Bergmann）和席勒（Schiller）引入了一个新颖的假设，这是出于量子重力的动机：可观察到的是_Invariant _invariant _invariant _ Intervariant _each个人_ Aeach个人_ Plassival _ Plassival _头等构造所产生的转换。尽管现代作品依靠伯格曼的权威，有时还说“伯格曼可观察到”，但他对可观察到的东西有很多话要说，这是合理的，但并非全部一致或记住。 有时，他需要可观察到的本地定义（不变和全球）；有时他希望他们独立于哈密顿形式主义（本质上不涉及单独的一流限制）。但是通常，他拿走了观察力，使每个一流的约束都消失了泊松支架，据称是通过电动力学证明的。他预计可观察到的物体将类似于电磁自由的横向真实程度。因此，他没有可靠地认可的可观察到的一致概念。 经过修订的可观察到的定义满足了等效理论应使用Rosenfeld-Anderson-bergmann-Castellani仪表发电机$ G $具有等效观察的要求，这是一流的一流约束总和，它会改变规范动作$ \ int $ \ int dt（p \ dot dot dt dt（p \ dot dot {q} -h）。从没有一流限制的理论表述中引导，GR的“外部”坐标对称要求协方差（$ 4 $二维的谎言衍生物），而不是不变性（$ 0 $ poisson bracket），$ g $以下（不是每个一流的约束）。
The problem of observables and their supposed lack of change has been significant in Hamiltonian quantum gravity since the 1950s. This paper considers the unrecognized variety of ideas about observables in the thought of Peter Bergmann, who invented observables. Whereas initially he required a constrained Hamiltonian formalism to be mathematically equivalent to the Lagrangian, in 1953 Bergmann and Schiller introduced a novel postulate, motivated by facilitating quantum gravity: observables were _invariant_ under transformations generated by _each individual_ first-class constraint. While modern works rely on Bergmann's authority and sometimes speak of "Bergmann observables," he had much to say about observables, plausible but not all consistent or remembered. At times he required observables to be locally defined (not changeless and global); at times he wanted them independent of the Hamiltonian formalism (not essentially involving separate first-class constraints). But typically he took observables to have vanishing Poisson bracket with each first-class constraint, purportedly justified by electrodynamics. He expected observables to be analogous to the transverse true degrees of freedom of electromagnetism. Hence there is no coherent concept of observables which he reliably endorsed. A revised definition of observables that satisfies the requirement that equivalent theories should have equivalent observables using the Rosenfeld-Anderson-Bergmann-Castellani gauge generator $G$, a tuned sum of first-class constraints that changes the canonical action $\int dt(p\dot{q}-H)$ by a boundary term. Bootstrapping from theory formulations with no first-class constraints, the "external" coordinate symmetry of GR calls for covariance ($4$-dimensional Lie derivative), not invariance ($0$ Poisson bracket), under $G$ (not each first-class constraint).
