论文标题
高阶Feynman图中的典型符号结构
Fermionic Sign Structure of High-order Feynman diagrams in a Many-fermion System
论文作者
论文摘要
散射振幅之间取消的符号使费米子不同于玻色子。我们系统地研究了代表性的多个特色系统中Feynman图的费米子符号结构---均匀的费米气体与Yukawa相互作用。我们分析了交叉对称性和全局仪表对称性在费米子取消中的作用。然后，使用对称参数来识别图表的符号符号组。符号结构分析有两种应用。从数值上讲，它导致用于快速图评估的群集图蒙特卡洛算法。新算法的价格约为$ 10^5美元，比第六阶的传统方法快。此外，我们的分析为构建众多特性系统的相关有效现场理论提供了重要的提示。
The sign cancellation between scattering amplitudes makes fermions different from bosons. We systematically investigate Feynman diagrams' fermionic sign structure in a representative many-fermion system---a uniform Fermi gas with Yukawa interaction. We analyze the role of the crossing symmetry and the global gauge symmetry in the fermionic sign cancellation. The symmetry arguments are then used to identify the sign-canceled groups of diagrams. Sign-structure analysis has two applications. Numerically, it leads to a cluster diagrammatic Monte Carlo algorithm for fast diagram evaluations. The new algorithm is about $10^5$ times faster than the conventional approaches in the sixth order. Furthermore, our analysis provides important hints in constructing the relevant effective field theory for many-fermion systems.
