标题： 研究在格点上使用径向量子化的$\textrm{QED}_3$—— I. 自由极限 显示英文标题

标题： Studying $\textrm{QED}_3$ with radial quantization on the lattice -- I. Free limit

摘要： 为了研究径向量子化下的三维量子电动力学，构建了格点作用量并在$S^2 \times \mathbb{R}$上研究了自由极限。 通过重叠费米子，数值验证了理论的重要对称性可以在格点上实现。 导出了解析关联函数并与格点结果进行了比较，包括整体归一化在内都一致。 在连续极限中确认了$O(a^2)$-缩放趋向于解析值，并对前几级细化水平所再现的次级态数量进行了启发式的估计。 我们的研究帮助我们识别了在二十面体格点上无需微调即可研究的理论特征。 显示英文摘要

摘要： To investigate the three-dimensional quantum electrodynamics in the radial quantization on the lattice, the lattice action is constructed and the free limit is studied on $S^2 \times \mathbb{R}$. With the overlap fermion, it is numerically verified that the important symmetries of the theory can be realized on the lattice. The analytic correlators are derived and compared to the lattice results, which agree including the overall normalization. The $O(a^2)$-scaling is confirmed toward the analytic value in the continuum limit, and the number of reproduced descendant states is estimated heuristically for the first few refinement levels. Our study helps us identify the features of the theory that we can study on the icosahedral lattice without fine-tuning.