论文标题
从一个空间维度中的量子细胞自动机和较高尺寸的无关定理的量子场理论
Quantum field theory from a quantum cellular automaton in one spatial dimension and a no-go theorem in higher dimensions
论文作者
论文摘要
已经表明，某些量子步行会产生相对论波动方程，例如狄拉克和Weyl方程，以其长波长极限。这个有趣的结果提出了一个问题，即在多粒子情况下是否会发生类似的事情。我们构建了一个一维量子细胞自动机（QCA）模型，该模型与单个粒子情况下的量子行走匹配，并在长波长极限下接近自由费米的量子场理论。但是，我们表明，这种类别的构造并未以任何直接的方式推广到更高的空间维度，并且在两个或多个空间维度中不可能具有相似特性的结构。这排除了基于QCA的最常见方法。我们建议可能在保留当地的同时克服这一障碍的可能方法。
It has been shown that certain quantum walks give rise to relativistic wave equations, such as the Dirac and Weyl equations, in their long-wavelength limits. This intriguing result raises the question of whether something similar can happen in the multi-particle case. We construct a one-dimensional quantum cellular automaton (QCA) model which matches the quantum walk in the single particle case, and which approaches the quantum field theory of free fermions in the long-wavelength limit. However, we show that this class of constructions does not generalize to higher spatial dimensions in any straightforward way, and that no construction with similar properties is possible in two or more spatial dimensions. This rules out the most common approaches based on QCAs. We suggest possible methods to overcome this barrier while retaining locality.
