论文标题
弯曲空间中操作员产品扩展的递归结构
Recursive construction of the operator product expansion in curved space
论文作者
论文摘要
我得出了一个在任意弯曲空间中运算符产品扩展系数（Wilson ope系数）系数的耦合组合衍生物的公式，作为量子作用原理的自然扩展。以耦合常数的力量扩展系数本身，该公式允许将它们递归地计算为任意秩序。作为输入，仅需要自由理论中的OPE系数，使用Wick的定理很容易获得。我通过计算两个标量$ ϕ $在双曲空间（Euclidean anti Anti-De安静的空间）的操作来说明该方法，直到在四分之一相互作用$ Gϕ^4 $中分离到第一阶的平方的术语更快地消失了在$ g $中。
I derive a formula for the coupling-constant derivative of the coefficients of the operator product expansion (Wilson OPE coefficients) in an arbitrary curved space, as the natural extension of the quantum action principle. Expanding the coefficients themselves in powers of the coupling constants, this formula allows to compute them recursively to arbitrary order. As input, only the OPE coefficients in the free theory are needed, which are easily obtained using Wick's theorem. I illustrate the method by computing the OPE of two scalars $ϕ$ in hyperbolic space (Euclidean Anti-de Sitter space) up to terms vanishing faster than the square of their separation to first order in the quartic interaction $g ϕ^4$, as well as the OPE coefficient $\mathcal{C}^{\mathbb{1}}_{ϕϕ}$ at second order in $g$.
