一种随机求根方法：应用于Dyson-Schwinger方程的同伦分析方法
A stochastic root finding approach: The Homotopy Analysis Method applied to Dyson-Schwinger Equations
摘要：
我们提出了根树图的建设和随机求和，根查找算法应用于戴森-Schwinger方程（DSEs）的基础上扩展。的数学公式显示出优越的收敛性能相比，大胆的图解蒙特卡罗方法和开发的算法允许一个通用的高维积分方程，以避免明确处理高维对象的诅咒，并访问非微扰制度。符号问题仍然是一个限制因素，但并不比其他方法更糟。我们举例说明$ϕ^4$理论的方法，但注意到它原则上适用于任何模型。
英文摘要：
We present the construction and stochastic summation of rooted-tree diagrams, based on the expansion of a root finding algorithm applied to the Dyson-Schwinger equations (DSEs). The mathematical formulation shows superior convergence properties compared to the bold diagrammatic Monte Carlo approach and the developed algorithm allows one to tackle generic high-dimensional integral equations, to avoid the curse of dealing explicitly with high-dimensional objects and to access non-perturbative regimes. The sign problem remains the limiting factor, but it is not found to be worse than in other approaches. We illustrate the method for $ϕ^4$ theory but note that it applies in principle to any model.
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