标题： 局部量子，幺正不等价性，真空纠缠 显示英文标题

标题： Local quanta, unitary inequivalence, and vacuum entanglement

摘要： 在本工作中，我们发展了一种形式化方法，用于描述一维盒子中的实值克莱因-戈登场的局域量子。$[0, R]$。 我们使用非定态局域模式对场进行量子化，在某个任意选择的初始时刻，这些模式完全局域于盒子的左侧或右侧。 在这个具体设置中，我们直接面对通常被视为基本粒子的局域场激发概念所固有的问题。 具体而言，通过计算将局域和标准（全局）量子化相关联的布戈利乌博夫系数，我们证明局域量子化产生了一个与标准量子化单位不等价的福克空间$\mathfrak F^L$$\mathfrak F^G$。 尽管如此，我们发现局域创建者和湮灭者在全局福克空间$\mathfrak F^G$中仍然定义良好，与盒子左右部分相关的局域数算符也是如此。 我们最终得到了一个有用的数学工具箱，用于分析和表征$\mathfrak F^G$中量子态的局域特征。 具体而言，根据局域数算符对全局真空态$|0_G\rangle\in\mathfrak F^G$的分析表明，如预期的那样，盒子左右区域之间存在纠缠。 相反，局域真空$|0_L\rangle\in\mathfrak F^L$具有非常不同的特性。 它既不是循环的也不是分离的，并且没有纠缠。 进一步的分析表明，全局真空也表现出一种类似于热浴的局域激发分布。 我们讨论了在此开发的数学工具如何可能为局部量子场论中的基本问题分析开辟新的途径。 显示英文摘要

摘要： In this work we develop a formalism for describing localised quanta for a real-valued Klein-Gordon field in a one-dimensional box $[0, R]$. We quantise the field using non-stationary local modes which, at some arbitrarily chosen initial time, are completely localised within the left or the right side of the box. In this concrete set-up we directly face the problems inherent to a notion of local field excitations, usually thought of as elementary particles. Specifically, by computing the Bogoliubov coefficients relating local and standard (global) quantizations, we show that the local quantisation yields a Fock space $\mathfrak F^L$ which is unitarily inequivalent to the standard one $\mathfrak F^G$. In spite of this, we find that the local creators and annihilators remain well defined in the global Fock space $\mathfrak F^G$, and so do the local number operators associated to the left and right partitions of the box. We end up with a useful mathematical toolbox to analyse and characterise local features of quantum states in $\mathfrak F^G$. Specifically, an analysis of the global vacuum state $|0_G\rangle\in\mathfrak F^G$ in terms of local number operators shows, as expected, the existence of entanglement between the left and right regions of the box. The local vacuum $|0_L\rangle\in\mathfrak F^L$, on the contrary, has a very different character. It is neither cyclic nor separating and displays no entanglement. Further analysis shows that the global vacuum also exhibits a distribution of local excitations reminiscent, in some respects, of a thermal bath. We discuss how the mathematical tools developed herein may open new ways for the analysis of fundamental problems in local quantum field theory.