标题： 彼得·伯格曼关于哈密顿广义相对论中的可观测量：一项历史批判性研究 显示英文标题

标题： Peter Bergmann on Observables in Hamiltonian General Relativity: A Historical-Critical Investigation

摘要： 可观测量及其似乎不变的问题自20世纪50年代以来在哈密顿量子引力中一直很重要。 本文考虑了彼得·伯格曼思想中关于可观测量的未被认识到的各种观点，他是可观测量的发明者。 起初他要求约束哈密顿形式与拉格朗日形式在数学上等价，但在1953年伯格曼和施利尔引入了一个新假设，这是为了促进量子引力：可观测量在由每个单独的一阶约束生成的变换下是_不变的_。 虽然现代研究依赖于伯格曼的权威，有时会提到“伯格曼可观测量”，但他对可观测量有很多论述，这些论述有道理但并非全部一致或被记住。 有时他要求可观测量是局部定义的（不是不变的和全局的）；有时他希望它们独立于哈密顿形式（不涉及单独的一阶约束）。 但通常他将可观测量视为与每个一阶约束的泊松括号为零，这据说是由电动力学所证明的。 他期望可观测量类似于电磁学中横向真实自由度。 因此，他可靠支持的可观测量概念并不连贯。 一种修正的可观测量定义，满足等效理论应具有等效可观测量的要求，使用了罗斯纳尔德-安德森-伯格曼-卡斯特拉尼规范生成器$G$，这是一个一阶约束的调和和，通过边界项改变正则作用$\int dt(p\dot{q}-H)$。 从没有一阶约束的理论表述进行自举，广义相对论的“外部”坐标对称性要求协变性 ($4$维李导数)，而不是不变性 ($0$泊松括号)，在$G$（而不是每个一阶约束）下。 显示英文摘要

摘要： 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).