标题： 三维$φ^4$理论的径向格点量子化算符乘积展开 显示英文标题

标题： The Operator Product Expansion for Radial Lattice Quantization of 3D $φ^4$ Theory

摘要： 在它的临界点处，三维晶格Ising模型由一个共形场论（CFT）描述，即3d Ising CFT。我们使用量子有限元方法，在逼近 $\phi^4$ 的单纯形晶格上实现径向量化临界 $\mathbb{R} \times S^2$ 理论，而不是在欧几里得晶格上进行模拟。 计算相同标量的四点函数时，我们通过准确确定三维伊辛 CFT 中的第一个自旋为 0 和自旋为 2 的主要算符 $\epsilon$ 和 $T$ 的尺度维度 $\Delta_{\epsilon}$ 和 $\Delta_{T}$ 以及算符乘积展开（OPE）系数比值 $f_{\sigma \sigma \epsilon}$ 和 $f_{\sigma \sigma T}$，展示了径向量化的优势。 显示英文摘要

摘要： At its critical point, the three-dimensional lattice Ising model is described by a conformal field theory (CFT), the 3d Ising CFT. Instead of carrying out simulations on Euclidean lattices, we use the Quantum Finite Elements method to implement radially quantized critical $\phi^4$ theory on simplicial lattices approaching $\mathbb{R} \times S^2$. Computing the four-point function of identical scalars, we demonstrate the power of radial quantization by the accurate determination of the scaling dimensions $\Delta_{\epsilon}$ and $\Delta_{T}$ as well as ratios of the operator product expansion (OPE) coefficients $f_{\sigma \sigma \epsilon}$ and $f_{\sigma \sigma T}$ of the first spin-0 and spin-2 primary operators $\epsilon$ and $T$ of the 3d Ising CFT.