论文标题
欧几里得路径积分状态的模块化哈密顿量
Modular Hamiltonians for Euclidean Path Integral States
论文作者
论文摘要
我们研究半空间/RINDLER模块化的哈密顿量，用于通过在相对论量子场理论中为欧几里得路径积分中的本地操作员打开源来创建的激发状态。我们为模块化的哈密顿量提供了一个简单的，显然是洛伦兹的公式，以供该来源中的所有扰动理论中的所有顺序。我们将此公式应用于真空状态下形状的半空间的情况下，并以半侧无效量算子的产物（即，应力张量张力组件（即沿未来和过去的Rindler Horizons）集成的应力张量成分，将相应的模块化汉密尔顿式化合物用于形状变形中的所有订单。在形状变形纯粹为空的特殊情况下，我们的扰动序列可以重新亮相，并且与已知的真空模块化汉密尔顿（Hamiltonians for Rindler Horizon）无效的真空模块化汉密尔顿人的已知公式一致。最后，我们研究了保形场理论中相关函数中的本地运算符模块流（对应于欧几里得路径积分状态）的一些通用性能。特别是，我们展示了流动如何变为局部提升，而在该极限中，流动的操作员接近纠缠。
We study half-space/Rindler modular Hamiltonians for excited states created by turning on sources for local operators in the Euclidean path integral in relativistic quantum field theories. We derive a simple, manifestly Lorentzian formula for the modular Hamiltonian to all orders in perturbation theory in the sources. We apply this formula to the case of shape-deformed half spaces in the vacuum state, and obtain the corresponding modular Hamiltonian to all orders in the shape deformation in terms of products of half-sided null energy operators, i.e., stress tensor components integrated along the future and past Rindler horizons. In the special case where the shape deformation is purely null, our perturbation series can be resummed, and agrees precisely with the known formula for vacuum modular Hamiltonians for null cuts of the Rindler horizon. Finally, we study some universal properties of modular flow (corresponding to Euclidean path integral states) of local operators inside correlation functions in conformal field theories. In particular, we show how the flow becomes the local boost in the limit where the operator being flowed approaches the entanglement cut.
