标题： 线性化（不）稳定性与交叉乘积 显示英文标题

标题： Linearization (in)stabilities and crossed products

摘要： 模交叉乘积代数最近在微扰量子引力中扮演了重要角色，因为它们通过引入量子参考系（QRFs）代替显式调节器，对纠缠熵实现了内在的正则化。这是通过在引力子、QRFs和其他场施加某些提升约束来实现的。在这里，我们通过微扰理论的视角重新审视这些约束应该如何理解，特别是线性化（不）稳定性研究，探讨线性化解何时可以积分到精确解。我们的目标是提供一些关于在各种条件下对线性化理论施加这些约束的合理性的清晰认识，在$G_N\to0$极限下，它们被证明是二阶的。虽然对于空间闭合时空，这种合理性基本上是明确的，但在存在边界或缺乏等距的情况下，这取决于是否也关注二阶可观测量。任何具有非线性方程的规范协变场论都会出现线性化（不）稳定性，为了在一个统一的框架中解决这个问题，我们将主题从通常的正则形式转换为系统化的协变相空间语言。这克服了特定理论的论点，揭示了（不）稳定性的普遍结构，并使我们能够涵盖任意的一般协变理论。我们评论了与模流的关系，并在几个引力和规范理论的例子中说明了我们的发现。 显示英文摘要

摘要： Modular crossed product algebras have recently assumed an important role in perturbative quantum gravity as they lead to an intrinsic regularization of entanglement entropies by introducing quantum reference frames (QRFs) in place of explicit regulators. This is achieved by imposing certain boost constraints on gravitons, QRFs and other fields. Here, we revisit the question of how these constraints should be understood through the lens of perturbation theory and particularly the study of linearization (in)stabilities, exploring when linearized solutions can be integrated to exact ones. Our aim is to provide some clarity about the status of justification, under various conditions, for imposing such constraints on the linearized theory in the $G_N\to0$ limit as they turn out to be of second-order. While for spatially closed spacetimes there is an essentially unambiguous justification, in the presence of boundaries or the absence of isometries this depends on whether one is also interested in second-order observables. Linearization (in)stabilities occur in any gauge-covariant field theory with non-linear equations and to address this in a unified framework, we translate the subject from the usual canonical formulation into a systematic covariant phase space language. This overcomes theory-specific arguments, exhibiting the universal structure behind (in)stabilities, and permits us to cover arbitrary generally covariant theories. We comment on the relation to modular flow and illustrate our findings in several gravity and gauge theory examples.