Spacetime path formalism: localized states

Schrödinger field theory in curved spacetime: In-In formalism and three-point function for inflationary background

We review the Schrödinger picture of field theory in curved spacetime and using this formalism, the power spectrum of massive non-interacting, minimally coupled scalars in a fixed de Sitter background is obtained. To calculate the N-point function in Schrödinger field theory, the "in-in" formalism is extended in the Friedmann-Lemaître-Robertson-Walker (FLRW) universe. We compute the three-point function for primordial scalar field fluctuation in the single field inflation by this in-in formalism. The results are the same as the three-point function in the Heisenberg picture.

Localizing and excluding quantum information; or, how to share a quantum secret in spacetime

When can quantum information be localized to each of a collection of spacetime regions, while also excluded from another collection of regions? We answer this question by defining and analyzing the localize-exclude task, in which a quantum system must be localized to a collection of authorized regions while also being excluded from a set of unauthorized regions. This task is a spacetime analogue of quantum secret sharing, with authorized and unauthorized regions replacing authorized and unauthorized sets of parties. Our analysis yields the first quantum secret sharing scheme for arbitrary acce…

Localized qubits in curved spacetimes

We provide a systematic and self-contained exposition of the subject of localized qubits in curved spacetimes. This research was motivated by a simple experimental question: if we move a spatially localized qubit, initially in a state |ψ_1>, along some spacetime path Γfrom a spacetime point x_1 to another point x_2, what will the final quantum state |ψ_2> be at point x_2? This paper addresses this question for two physical realizations of the qubit: spin of a massive fermion and polarization of a photon. Our starting point is the Dirac and Maxwell equations that describe respectively the one-p…

提取时空涨落的电磁特征

Extracting electromagnetic signatures of spacetime fluctuations

本文提出通过电磁场关联测量识别时空度规涨落效应的形式体系，并利用 Michelson 干涉仪数据约束真空折射率随机涨落模型，所得界限强于既有天文观测限制。

The arithmetic of uncertainty unifies quantum formalism and relativistic spacetime

The theories of quantum mechanics and relativity dramatically altered our understanding of the universe ushering in the era of modern physics. Quantum theory deals with objects probabilistically at small scales, whereas relativity deals classically with motion in space and time. We show here that the mathematical structures of quantum theory and of relativity follow together from pure thought, defined and uniquely constrained by the same elementary "combining and sequencing" symmetries that underlie standard arithmetic and probability. The key is uncertainty, which inevitably accompanies obser…

算子依赖性和量子临界自旋链中时空局域响应的鲁棒性

Operator dependence and robustness of spacetime-localized response in a quantum critical spin chain

该研究探讨了量子临界自旋链中时空局域响应的算子依赖性和鲁棒性，通过分析一维横向磁场异斯模型的实时动力学，揭示了特定扰动类型与局域化响应的关系，并展示了其在实验中的应用价值。

时空密度矩阵：形式体系与性质

Spacetime Density Matrix: Formalism and Properties

本文提出时空密度矩阵作为标准密度矩阵在多个柯西面之间的推广，建立其形式体系、路径积分表示和超算符框架，并推导运动方程及弱耦合下矩的微扰计算方法。

弯曲时空中的局域非相对论量子系统：粒子探测器模型的一般表征

Localized non-relativistic quantum systems in curved spacetimes: a general characterization of particle detector models

本研究利用费米法向坐标构建弯曲时空中沿类时轨迹运动的局域非相对论量子系统的自洽描述框架，给出粒子探测器模型的通用定义并明确其适用范围。

量子场论中曲率对局部可观测量影响

The effect of curvature on local observables in quantum field theory

研究时空局部曲率对质量实标量场平方振幅期望值主导阶修正，利用Riemann法坐标和Hadamard条件定义局部场算符并求曲率修正，应用于粒子探测器模型量化曲率影响。

广义相对论中的狄拉克方程与3+1形式体系

The Dirac equation in General Relativity and the 3+1 formalism

针对狄拉克方程在经典广义相对论中未被广泛纳入标准工具的情况，本文从闵可夫斯基时空出发，结合洛伦兹群与标架形式体系综述了弯曲时空中的狄拉克方程，并推导了3+1形式下的方程及应力-能量张量，为狄拉克场演化研究提供支撑。

Quasitemporal structure and symmetries in histories-based generalized quantum mechanics in curved spacetime

The formalism for histories-based generalized quantum mechanics developed in two earlier papers is applied to the treatment of histories (of particles or fields or more general objects) in curved spacetimes (which need not admit foliation in spacelike hypersurfaces). The construction of the space of temporal supports (a partial semigroup generalizing the space of finite time sequences employed in traditional temporal description of histories) employs spacelike subsets of spacetime having dimensionality less than or equal to three. Definition of symmetry is sharpened by the requirement of conti…

Emergent spacetime and empirical (in)coherence

Numerous approaches to a quantum theory of gravity posit fundamental ontologies that exclude spacetime, either partially or wholly. This situation raises deep questions about how such theories could relate to the empirical realm, since arguably only entities localized in spacetime can ever be observed. Are such entities even possible in a theory without fundamental spacetime? How might they be derived, formally speaking? Moreover, since by assumption the fundamental entities can't be smaller than the derived (since relative size is a spatiotemporal notion) and so can't 'compose' them in any or…

非厄米时空与广义热场双重形式

Non-Hermitian spacetime and generalized thermofield double formalism

本文研究非厄米跃迁矩阵及其引力对偶，证明η-赝厄米跃迁矩阵可替代密度矩阵，并在AdS/CFT中用于实现热场双重态、解释黑洞熵及赝熵的强次可加性。