论文标题
部分可观测时空混沌系统的无模型预测
Momentum-dependence in the infinitesimal Wilsonian renormalization group
论文作者
论文摘要
威尔逊对重新归一化组的原始表述本质上是扰动性的。 We here present an alternative derivation of the infinitesimal momentum shell RG, akin to the Wegner and Houghton scheme, that is a priori exact. We show that the momentum-dependence of vertices is key to obtain a diagrammatic framework that has the same one-loop structure as the vertex expansion of the Wetterich equation.动量依赖性导致截止参数中的延迟功能微分方程。 Approximations are then made at two points: truncation of the vertex expansion and approximating the functional form of the momentum dependence by a momentum-scale expansion. We exemplify the method on the scalar $φ^{4}$-theory, computing analytically the Wilson-Fisher fixed point, its anomalous dimension $η(d)$ and the critical exponent $ν(d)$ non-perturbatively in $d\in[3,4]$ dimensions.尽管方法简单，但结果与已知值的合理吻合。
Wilson's original formulation of the renormalization group is perturbative in nature. We here present an alternative derivation of the infinitesimal momentum shell RG, akin to the Wegner and Houghton scheme, that is a priori exact. We show that the momentum-dependence of vertices is key to obtain a diagrammatic framework that has the same one-loop structure as the vertex expansion of the Wetterich equation. Momentum dependence leads to a delayed functional differential equation in the cutoff parameter. Approximations are then made at two points: truncation of the vertex expansion and approximating the functional form of the momentum dependence by a momentum-scale expansion. We exemplify the method on the scalar $φ^{4}$-theory, computing analytically the Wilson-Fisher fixed point, its anomalous dimension $η(d)$ and the critical exponent $ν(d)$ non-perturbatively in $d\in[3,4]$ dimensions. The results are in reasonable agreement with the known values, despite the simplicity of the method.
