论文标题
De Sitter空间，极端表面和“时间到期”
de Sitter space, extremal surfaces and "time-entanglement"
论文作者
论文摘要
我们完善了先前对de de Sitter空间的调查，并锚定在未来边界$ i^+$的极端表面。由于此类表面没有返回，因此过去需要额外的数据或边界条件（内部）。在完全是洛伦兹（Lorentzian de Sitter Spacetime）中，这会导致未来的脉冲表面延伸到$ i^\ pm $之间。除了总体$ -i $ factor（相对于$ ADS $中的间距表面）外，它们的区域是真实而积极的。在没有边界的边界条件下，这些时间型表面的上半部分与半球的间距类似的部分连接在一起，可提供一个复杂的价值区域。由这些动机，我们在量子力学中简单的玩具模型中描述了“时间到期”的两个方面。一个基于未来的past热菲尔德双型状态纠缠序列类别的状态，这导致了完全积极的结构。另一个是基于时间演化算子和减少过渡幅度的，这导致了复杂的值熵。
We refine previous investigations on de Sitter space and extremal surfaces anchored at the future boundary $I^+$. Since such surfaces do not return, they require extra data or boundary conditions in the past (interior). In entirely Lorentzian de Sitter spacetime, this leads to future-past timelike surfaces stretching between $I^\pm$. Apart from an overall $-i$ factor (relative to spacelike surfaces in $AdS$) their areas are real and positive. With a no-boundary type boundary condition, the top half of these timelike surfaces joins with a spacelike part on the hemisphere giving a complex-valued area. Motivated by these, we describe two aspects of "time-entanglement" in simple toy models in quantum mechanics. One is based on a future-past thermofield double type state entangling timelike separated states, which leads to entirely positive structures. Another is based on the time evolution operator and reduced transition amplitudes, which leads to complex-valued entropy.
