AI 中文总结
研究在四维微分同胚不变理论中构建格劳伯-苏达山态，通过正则形式体系和路径积分分析其与相干态差异，检验构建一致性，表明其动力学受自举关系支配，还研究相关方程及态的结构解释。
AI 中文摘要
我们研究了在诸如具有零体哈密顿量且度规与额外自由度之间存在非平凡相互作用的四维微分同胚不变理论这样的高度受限系统中，如何在超对称极小值上构建瞬态激发态——即格劳伯-苏达山态。这些态一般是非超对称的，虽不是任何势的极小值，但允许有效模拟四维类德西特背景的正能量度规构型。我们通过在正则形式体系中借助边界哈密顿量研究其时间演化，以及在通过施温格-凯尔迪什轮廓的in-in路径积分框架中进行研究，来分析这些态与传统相干态的差异。我们还在三种互补描述间检验构建的一致性：1PI有效作用、威尔逊（或精确重整化群）有效作用以及施温格-凯尔迪什路径积分的皮卡-莱夫谢茨（莱夫谢茨缝杯）分解，后者提供了理论的跨级数组织。在存在规范固定和鬼场部分的情况下，我们表明这些瞬态构型的动力学由一个非平凡的自举关系支配，该关系同时约束它们在超对称闵可夫斯基真空附近以及沿类德西特轨迹的行为。最后，我们研究了惠勒-德维特方程、存在瞬态激发态时的时间概念以及体薛定谔方程的出现。我们进一步表明这些态允许一种类似于弦理论二维世界面表述中出现的顶点算符那样的自然结构解释。
英文摘要
We investigate how, in a highly constrained system such as a four-dimensional diffeomorphism-invariant theory with vanishing bulk Hamiltonian and non-trivial interactions between the metric and additional degrees of freedom, transient excited states--called Glauber-Sudarshan states--can be constructed over supersymmetric minima. These states are generically non-supersymmetric and, although they are not minima of any potential, they admit positive-energy metric configurations that effectively mimic four-dimensional quasi-de Sitter backgrounds. We analyze how such states differ from conventional coherent states by studying their time evolution both in the canonical formalism--via boundary Hamiltonians--and in the in-in path-integral framework through Schwinger-Keldysh contours. We also examine the consistency of the construction across three complementary descriptions: the 1PI effective action, the Wilsonian (or exact renormalization group) effective action, and the Picard-Lefschetz (Lefschetz-thimble) decomposition of the Schwinger-Keldysh path integral, which provides the trans-series organization of the theory. In the presence of gauge-fixing and ghost sectors, we show that the dynamics of these transient configurations are governed by a nontrivial bootstrap relation that simultaneously constrains their behavior near supersymmetric Minkowski vacua and along quasi-de Sitter-like trajectories. Finally, we examine the Wheeler-DeWitt equation, the notion of time in the presence of transient excited states, and the emergence of the bulk Schrodinger equation. We further show that these states admit a natural structural interpretation analogous to the vertex operators that arise in the two-dimensional world-sheet formulation of string theory.
Comments269 pages, 20 pdf figures, LaTex; v2: Sections 3.3 and 8.1.7 elaborated, typos corrected and references updated
