论文标题
使用Rindler时空测试量子场理论中的传播率
Test of Transitivity in Quantum Field theory using Rindler spacetime
论文作者
论文摘要
我们在Minkowski Spacetime $ \ cal {m} $中考虑了一个无数的标量字段，并在此空间中考虑两个Rindler楔子$ R_1 $和$ R_2 $。 $ r_2 $将$ r_1 $的权利移至距离$δ$。因此，我们拥有$ r_2 \ subset r_1 \ subset \ cal {m} $，带有符号$ \ subset $暗示量子子系统。我们使用两种独立的方式在$ r_2 $中找到降低的状态：a）通过评估$ \ cal {m} $从真空状态下的降低状态，该状态首先评估$ \ cal {m}的$ \ cal {m} $中的$ \ cal {m} $中的$ r_1 $ r_1 $ 1 $ r_1 $ r_1 $ r_1 $的状态，从而产生热密度矩阵，b），该状态在$ \ cal {m1 $ r_1 $ $ r_1 $ $ _1 $中的订单中产生$ \ cal {m。 顺序。在本文中，我们试图解决以下问题，这两种独立的方式是否在$ r_2 $中产生相同的减少状态。为此，我们设计了一种方法，该方法涉及将Rindler楔子$ r_1 $切割到两个域中，从而形成热菲尔德双重。其中一个域沿楔形$ r_2 $对齐，而另一个域则是$ r_1 $和$ r_2 $之间的钻石形构造。我们得出的结论是，这两种独立的方法都产生了两个不同的答案，并讨论了我们结果在倒塌物质形成的非超级黑洞之外的量子状态下的可能含义。
We consider a massless scalar field in Minkowski spacetime $\cal{M} $ in its vacuum state, and consider two Rindler wedges $R_1$ and $R_2$ in this space. $R_2$ is shifted to the right of $R_1$ by a distance $Δ$. We therefore have $R_2\subset R_1 \subset \cal{M}$ with the symbol $\subset$ implying a quantum subsystem. We find the reduced state in $R_2$ using two independent ways: a) by evaluation of the reduced state from vacuum state in $\cal{M}$ which yields a thermal density matrix, b) by first evaluating the reduced state in $R_1$ from $\cal{M} $ yielding a thermal state in $R_1$, and subsequently evaluate the reduced state in $R_2$ in that order of sequence. In this article we attempt to address the question whether both these independent ways yield the same reduced state in $R_2$. To that end, we devise a method which involves cleaving the Rindler wedge $R_1$ into two domains such that they form a thermofield double. One of the domains aligns itself along the wedge $R_2$ while the other is a diamond shaped construction between the boundaries of $R_1$ and $R_2$. We conclude that both these independent methods yield two different answers, and discuss the possible implications of our result in the context of quantum states outside a non-extremal black hole formed by collapsing matter.
