AI 中文总结
研究量子场论手征离散化中狄拉克QCA的费米子倍增问题，通过证明其存在及对比相关模型，还计算了FD修正模型的两点关联函数，揭示其简单结构，明确了该模型在不同相对论区域的优势。
AI 中文摘要
我们给出了确定性证明，即参考文献中用于量子模拟和量子场论（尤其是量子电动力学）算法基础的狄拉克量子元胞自动机（QCA）确实存在费米子倍增（FD），尽管其严重程度仅为离散时间标准格点规范理论（LGT）的三分之一。证明针对(1 + 1)D狄拉克 - QCA模型。我们表明狄拉克QCA的（单时间步）两点关联函数（格林函数）极其简单，与狄拉克方程的格林函数形成对比。我们还定性和定量地比较了狄拉克QCA与狄拉克费米子的连续时间LGT空间离散化在逼近朴素连续极限方面的情况。在工作的第二部分，我们计算了最后引用参考文献中提出的FD修正模型（风味狄拉克QCA）两点关联函数，其结构极其简单，能用原始模型格林函数的四个手征分量非常简单地表示。
英文摘要
We give the definitive proof that the Dirac Quantum Cellular Automaton (QCA) used for both quantum simulation and algorithmic foundations of Quantum Field Theory (QFT), and especially of Quantum Electrodynamics (QED), as put forward in References https://doi.org/10.1007/s11128-019-2555-4 and https://doi.org/10.22331/q-2023-11-08-1179, does exhibit Fermion Doubling (FD), albeit thrice as less severe as discrete-time standard Lattice Gauge Theories (LGTs) [arXiv:2505.0790], which are naive regarding the spacetime discretization of differential operators acting on fermionic fields. The proof is done for the (1 + 1)D Dirac-QCA model. We show that the (one-time-step) two-point correlation function, also called Green's function (GF), of the Dirac QCA, is of astonishing simplicity, which is in contrast with the GF of the Dirac equation. We also compare, both qualitatively and quantitatively, this Dirac QCA to the continuous-time-LGT spatial discretization of Dirac fermions regarding how well these two lattice models approximate their naive continuum limit$\unicode{x2014}$which is nothing but the Dirac equation$\unicode{x2014}$even when far away from that limit, a situation which must be considered because of experimental limitations in quantum simulation: the Dirac QCA is better for ultrarelativistic regimes, whereas continuous-time LGT is better for non-relativistic regimes. Then, we compute the GF of the FD-fixed model put forward in the last cited reference, called Flavored Dirac QCA (FDQCA)$\unicode{x2014}$which staggers an extra, artificial flavor $only$, on a diamond spacetime lattice, and does not stagger chirality as staggered fermions in usual LGT. The structure of this FDQCA two-point correlation function is of extreme simplicity, and can be expressed in a very simple manner in terms of the four chiral components of the FD-suffering, original-model GF.
Comments26 pages. 14 pages for the body of the article. 12 pages of appendices. 3 figures related to the body of the article. 2 figures in the appendices
