论文标题
Hopf-Elgebraic Dyson-Schwinger方程的非扰动完成
Non-Perturbative Completion of Hopf-Algebraic Dyson-Schwinger Equations
论文作者
论文摘要
对于某些量子场理论，重新归一化的Kreimer-connes Hopf - gengebraic方法可将dyson-Schwinger方程降低到非线性普通微分方程的系统，以换取重态化绿色功能的扩展系数。我们采用复兴的渐近分析来找到跨系列解决方案，这些解决方案可提供这些正式的戴森 - 辛格替补的非扰动完成。我们用四维无质量宽川理论的具体示例说明了总体方法，并与Broadhurst和Kreimer发现的确切功能解决方案相连。跨系列解决方案与Dyson-Schwinger方程的迭代形式相关联，并显示了整数重复的Borel单数字的肾上腺样结构。由于我们称之为“功能复苏”的属性，可以提取Stokes常数。
For certain quantum field theories, the Kreimer-Connes Hopf-algebraic approach to renormalization reduces the Dyson-Schwinger equations to a system of non-linear ordinary differential equations for the expansion coefficients of the renormalized Green's function. We apply resurgent asymptotic analysis to find the trans-series solutions which provide the non-perturbative completion of these formal Dyson-Schwinger expansions. We illustrate the general approach with the concrete example of four dimensional massless Yukawa theory, connecting with the exact functional solution found by Broadhurst and Kreimer. The trans-series solution is associated with the iterative form of the Dyson-Schwinger equations, and displays renormalon-like structure of integer-repeated Borel singularities. Extraction of the Stokes constant is possible due to a property we call `functional resurgence'.
