论文标题
同位作用：收敛图理论的途径
Homotopic Action: A Pathway to Convergent Diagrammatic Theories
论文作者
论文摘要
阻止Feynman图解扩展准确地解决众所周知的综合系统的主要障碍是系列缓慢收敛或发散问题。已经提出了几种解决此问题的技术：通过共形映射通过移动的动作工具来改变扩展的起点的性质，并将同型分析方法应用于Dyson-Schwinger方程。它们成为针对问题的不同方面的数学程序不同。提出的同型动作提供了一个通用和系统的框架，用于统一现有的（并生成新的方法和想法），以根据收敛的图表系列制定物理系统。它消除了重新调整的需求，使人们能够引入有效的相互作用，实现连续空间理论的受控紫外线正规化，并降低了图解蒙特卡洛方法的固有多项式复杂性。我们通过应用于Hubbard模型的应用来说明这种方法。
The major obstacle preventing Feynman diagrammatic expansions from accurately solving many-fermion systems in strongly correlated regimes is the series slow convergence or divergence problem. Several techniques have been proposed to address this issue: series resummation by conformal mapping, changing the nature of the starting point of the expansion by shifted action tools, and applying the homotopy analysis method to the Dyson-Schwinger equation. They emerge as dissimilar mathematical procedures aimed at different aspects of the problem. The proposed homotopic action offers a universal and systematic framework for unifying the existing -- and generating new -- methods and ideas to formulate a physical system in terms of a convergent diagrammatic series. It eliminates the need for resummation, allows one to introduce effective interactions, enables a controlled ultraviolet regularization of continuous-space theories, and reduces the intrinsic polynomial complexity of the diagrammatic Monte Carlo method. We illustrate this approach by an application to the Hubbard model.
