标题： 可观测量与规范不变性在非线性时空扰动理论中的作用 显示英文标题

标题： Observables and gauge invariance in the theory of non-linear spacetime perturbations

摘要： 我们讨论广义相对论摄动理论中的可观测量问题，采用的观点是广义相对论中的任何可观测量都由时空上的标量场表示。 在摄动理论的背景下，可观测量因此是扰动时空上的标量场，因此在精确意义上（所有阶次）是规范不变的，这符合预期。 然而，通常用背景时空上的场来表示扰动，并在不同阶次展开为可能具有或不具有规范独立性的贡献。 我们证明，标量量的扰动如果是一阶规范不变的，则是可观测量，即使它们在更高阶次时可能是规范依赖的。 因此，一阶规范不变性在理论上起着重要的概念作用，因为它从仅具有数学意义的扰动中选取了具有直接物理意义的扰动。 所谓的“规范问题”以及测量到的涨落与理论中计算出的规范依赖扰动之间的关系也得到了澄清。 显示英文摘要

摘要： We discuss the issue of observables in general-relativistic perturbation theory, adopting the view that any observable in general relativity is represented by a scalar field on spacetime. In the context of perturbation theory, an observable is therefore a scalar field on the perturbed spacetime, and as such is gauge invariant in an exact sense (to all orders), as one would expect. However, perturbations are usually represented by fields on the background spacetime, and expanded at different orders into contributions that may or may not be gauge independent. We show that perturbations of scalar quantities are observable if they are first order gauge-invariant, even if they are gauge dependent at higher order. Gauge invariance to first order plays therefore an important conceptual role in the theory, for it selects the perturbations with direct physical meaning from those having only a mathematical status. The so-called ``gauge problem'', and the relationship between measured fluctuations and gauge dependent perturbations that are computed in the theory are also clarified.