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Non-perturbative completion of Hopf-algebraic Dyson-Schwinger equations
Nuclear Physics B ( IF 2.8 ) Pub Date : 2020-06-25 , DOI: 10.1016/j.nuclphysb.2020.115096
Michael Borinsky , Gerald V. Dunne

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’.



中文翻译:

Hopf代数Dyson-Schwinger方程的非摄动完成

对于某些量子场论,用于重归一化的Kreimer-Connes Hopf-代数方法将Dyson-Schwinger方程简化为非线性常微分方程组,用于重新归一化的格林函数的展开系数。我们应用中兴渐近分析来找到跨序列解,这些解提供了这些戴森-舒温格形式正则展开的非扰动完成。我们以四维无质量Yukawa理论的具体示例为例,并结合Broadhurst和Kreimer找到的精确函数解来说明通用方法。跨级数解与Dyson-Schwinger方程的迭代形式相关联,并显示整数重复的Borel奇点的类似renormalon的结构。

更新日期:2020-06-30
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