从量子元胞自动机中解放量子场论：Weyl，Dirac和Maxwell量子元胞自动机的推导
Free quantum field theory from quantum cellular automata: derivation of Weyl, Dirac and Maxwell quantum cellular automata
摘要：
在导致量子理论的一个新的公理化推导之后，新的信息范式正在进入量子场论的领域，提出了一个量子自动机框架，可以被视为量子场论的扩展，以包括一个假设的普朗克尺度，并与通常的量子场论恢复在小波矢量的相对论极限。自动机理论源自简单的原理（线性、么正性、局部性、均匀性、各向同性和维数最小），是量子从头算，不假设洛伦兹协变性和力学概念。由于是离散的，它可以描述局域态和测量（量子场论无法处理），解决了场论起源于连续统的所有问题。这些特征使该理论成为量子引力的理想框架，相对论协变性和时空仅从相互作用中涌现，而不是先验假设。本文介绍了自动机理论的综合推导，展示了如何从原理中推导出群的凯莱图上的量子自动机的描述。限制阿贝尔群，我们展示了如何自动机恢复外尔，狄拉克和麦克斯韦动力学的相对论极限。我们得出结论，一些新的路线更一般的情况下，非阿贝尔凯莱图。
英文摘要：
After leading to a new axiomatic derivation of quantum theory, the new informational paradigm is entering the domain of quantum field theory, suggesting a quantum automata framework that can be regarded as an extension of quantum field theory to including an hypothetical Planck scale, and with the usual quantum field theory recovered in the relativistic limit of small wave-vectors. Being derived from simple principles (linearity, unitarity, locality, homogeneity, isotropy, and minimality of dimension), the automata theory is quantum ab-initio, and does not assume Lorentz covariance and mechanical notions. Being discrete it can describe localized states and measurements (unmanageable by quantum field theory), solving all the issues plaguing field theory originated from the continuum. These features make the theory an ideal framework for quantum gravity, with relativistic covariance and space-time emergent solely from the interactions, and not assumed a priori. The paper presents a synthetic derivation of the automata theory, showing how from the principles lead to a description in terms of a quantum automaton over a Cayley graph of a group. Restricting to Abelian groups we show how the automata recover the Weyl, Dirac and Maxwell dynamics in the relativistic limit. We conclude with some new routes about the more general scenario of non-Abelian Cayley graphs.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
