Non-perturbative completion of Hopf-algebraic Dyson-Schwinger equations
Non-perturbative completion of Hopf-algebraic Dyson-Schwinger equations
复制标题
Hopf 代数 Dyson-Schwinger 方程的非微扰完备
DOI：
10.1016/j.nuclphysb.2020.115096
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发表时间：
2020
影响因子：
2.8
通讯作者：
G. Dunne
中科院分区：
文献类型：
--
作者：
M. Borinsky;G. Dunne
对于某些量子场论，重整化的Kreimer-Connes霍普夫代数方法将戴森-施温格方程简化为重整化绿色函数展开系数的非线性常微分方程组。我们应用复苏渐近分析，找到反级数的解决方案，提供非微扰完成这些正式的戴森-Schwinger展开。我们用四维无质量汤川理论的具体例子说明了一般方法，并与Broadhurst和Kreimer发现的精确泛函解相联系。反级数解与Dyson-Schwinger方程的迭代形式相关联，并显示出整数重复的Borel奇点的类重正马龙结构。斯托克斯常数的提取是可能的，由于我们称之为“功能性再生”的属性。
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’.