标题： 关于视角中性、代数和有效量子参考系之间的关系 显示英文标题

标题： On the relation between perspective-neutral, algebraic, and effective quantum reference frames

摘要： 内部量子参考系(QRFs)的框架构成了处理量子理论中对称性的通用工具集，并在量子引力、规范理论和基础物理领域带来了新的发现。 多种方法已经出现，有时在范围和对称性实现方式上有所不同，引发了它们之间关系的问题。 在这里，我们研究了针对规范对称性的三种QRF方法之间的关系，即有效半经典方法、代数方法和视角中立(PN)方法。 与PN方法构建希尔伯特空间不同，有效方法基于由期望值和涨落参数化的量子相空间，而代数方法的重点是动力学代数上的复线性泛函的状态空间。 然而，在所有三种形式化中，外部框架信息都被视为规范，这体现在状态和代数上的约束上。 我们证明，这三种方法实际上对于理想的QRF是等价的，这些QRF具有尖锐的方向性，这是前两种方法的先前设置。 我们的论证涉及单个约束，包括相对论性的约束，并涵盖了QRF的变化。 特别是，PN框架中的QRF变换在半经典意义上与较早的有效方法中的变换一致，后者是其灵感来源。 作为物理应用，我们探讨了不确定性与涨落的QRF协变性，结果表明它们是框架依赖的。 这特别适合有效方法和代数方法，因为这些量在其基础上自然形成。 最后，我们通过研究Page-Wootters形式化中的投影和规范固定操作，该形式化嵌入在PN框架中，作用于代数状态上，为将这两种方法扩展到非理想QRF铺平了道路。 显示英文摘要

摘要： The framework of internal quantum reference frames (QRFs) constitutes a universal toolset for dealing with symmetries in quantum theory and has led to new revelations in quantum gravity, gauge theories and foundational physics. Multiple approaches have emerged, sometimes differing in scope and the way symmetries are implemented, raising the question as to their relation. Here, we investigate the relation between three approaches to QRFs for gauge symmetries, namely the effective semiclassical, algebraic, and perspective-neutral (PN) approaches. Rather than constructing Hilbert spaces, as the PN approach, the effective approach is based on a quantum phase space parametrized by expectation values and fluctuations, while the emphasis of the algebraic approach is on the state space of complex linear functionals on a kinematical algebra. Nevertheless, external frame information is treated as gauge in all three formalisms, manifested in constraints on states and algebra. We show that these three approaches are, in fact, equivalent for ideal QRFs, distinguished by sharp orientations, which is the previous setting of the first two approaches. Our demonstration pertains to single constraints, including relativistic ones, and encompasses QRF changes. In particular, the QRF transformations of the PN framework agree semiclassically with those of the older effective approach, by which it was inspired. As a physical application, we explore the QRF covariance of uncertainties and fluctuations, which turn out to be frame-dependent. This is particularly well-suited for the effective and algebraic approaches, for which these quantities form a natural basis. Finally, we pave the way towards extending these two approaches to non-ideal QRFs by studying the projection and gauge-fixing operations of the Page-Wootters formalism, built into the PN framework, on algebraic states.