两粒子不可约有效作用量与重约作用量：分析性质和自洽性
Two-particle irreducible effective actions versus resummation: analytic properties and self-consistency
摘要：
基于两粒子不可约（2 PI）有效作用量的近似（也称为$Φ$ -derivable，Cornwall-Jackiw-Tomboulis或Luttinger-Ward泛函，取决于上下文）已被广泛用于凝聚态和非平衡量子/统计场论，因为这种形式主义给出了一种鲁棒的，自洽的，非微扰的和系统可改进的方法，避免了长期时间演化的问题。2 PI近似的强度经常被描述为费曼图到无限阶的选择性重绘。然而，费曼图级数是渐近的，求和充其量是一个危险的过程。在这里，我们表明，至少在一个玩具模型的上下文中，确切的结果是可用的，真正的实力2 PI近似来自他们的自我一致性，而不是任何重申。这种自洽性允许截断的2 PI近似来捕获物理振幅的分支点，其中耦合常数的调整可以触发真空的不稳定性。这实际上把戴森关于微扰论失败的论点颠倒过来了。结果表明，2 PI近似比Padé近似有更好的性能，并且与Borel-Padé近似具有竞争力。最后，我们介绍了一种混合2 PI-Padé方法。
英文摘要：
Approximations based on two-particle irreducible (2PI) effective actions (also known as $Φ$-derivable, Cornwall-Jackiw-Tomboulis or Luttinger-Ward functionals depending on context) have been widely used in condensed matter and non-equilibrium quantum/statistical field theory because this formalism gives a robust, self-consistent, non-perturbative and systematically improvable approach which avoids problems with secular time evolution. The strengths of 2PI approximations are often described in terms of a selective resummation of Feynman diagrams to infinite order. However, the Feynman diagram series is asymptotic and summation is at best a dangerous procedure. Here we show that, at least in the context of a toy model where exact results are available, the true strength of 2PI approximations derives from their self-consistency rather than any resummation. This self-consistency allows truncated 2PI approximations to capture the branch points of physical amplitudes where adjustments of coupling constants can trigger an instability of the vacuum. This, in effect, turns Dyson's argument for the failure of perturbation theory on its head. As a result we find that 2PI approximations perform better than Padé approximation and are competitive with Borel-Padé resummation. Finally, we introduce a hybrid 2PI-Padé method.
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