论文标题
3d $ ϕ^4 $ field理论的径向晶格量化
Radial Lattice Quantization of 3D $ϕ^4$ Field Theory
论文作者
论文摘要
经典有限元的量子扩展，称为量子有限元（{\ bf qfe}）实施明确的反词以取消一环紫外线缺陷以达到量子连续理论。使用Brower-tamayo〜 \ cite {Brower：1989Mt}集群Monte Carlo算法，数值结果支持QFE ANSATZ，即在连续体中达到关键的保形场理论（CFT），并具有$ \ MATHBB R \ times \ times \ times \ m m iathbb s^2 $ Restored $ \ mathbb r \ sathbb s^2 $ restored。 RICCI曲率项在技术上与量子理论无关，但显示出可极大地改善收敛开口的，这是确定CFT数据的高精度蒙特卡洛模拟的方式：操作员尺寸，三线性OPE耦合和中央电荷。
The quantum extension of classical finite elements, referred to as quantum finite elements ({\bf QFE})~\cite{Brower:2018szu,Brower:2016vsl}, is applied to the radial quantization of 3d $ϕ^4$ theory on a simplicial lattice for the $\mathbb R \times \mathbb S^2$ manifold. Explicit counter terms to cancel the one- and two-loop ultraviolet defects are implemented to reach the quantum continuum theory. Using the Brower-Tamayo~\cite{Brower:1989mt} cluster Monte Carlo algorithm, numerical results support the QFE ansatz that the critical conformal field theory (CFT) is reached in the continuum with the full isometries of $\mathbb R \times \mathbb S^2$ restored. The Ricci curvature term, while technically irrelevant in the quantum theory, is shown to dramatically improve the convergence opening, the way for high precision Monte Carlo simulation to determine the CFT data: operator dimensions, trilinear OPE couplings and the central charge.
