四维φ⁴模型非微扰二阶平均场理论中的平凡性
Triviality in a Non-Perturbative Second-Order Mean-Field Theory for $ϕ^4_4$
AI总结：
该研究在Wilson-Polchinski重整化群框架下构建四维φ⁴模型的非微扰二阶平均场理论，证明其非线性层级解的存在性与收敛性，发现相关动量分量为渐近平凡的。
AI中文摘要：
我们在Wilson-Polchinski重整化群框架下，引入了四维欧几里得φ⁴模型的二阶平均场描述。该构造基于在对称动量构型(p,-p,…,p,-p)处计算的连通截断施温格函数，将其分解为与动量无关的分量、p的二次项分量及高阶余项。前两个分量被选为满足闭合非线性层级的解。我们证明了该层级对任意正裸耦合存在解，并建立了当紫外截断移除时解向高斯不动点的收敛性。特别地，与动量无关的分量和二次动量分量均为渐近平凡的。
英文摘要：
We introduce a second-order mean-field description of the four-dimensional Euclidean $ϕ^4$ model within the Wilson--Polchinski renormalization-group framework. The construction is based on the connected amputated Schwinger functions evaluated at the symmetric momentum configurations $ (p,-p,\ldots,p,-p)$, which are decomposed into a momentum-independent component, a component quadratic in $p$, and a higher-order remainder. The first two components are chosen to satisfy a closed nonlinear hierarchy. We prove the existence of solutions to this hierarchy for arbitrary positive bare coupling and establish their convergence to the Gaussian fixed point as the ultraviolet cutoff is removed. In particular, both the momentum-independent and the quadratic momentum sectors are asymptotically trivial.
