零维时空中自能泛函的骨架级数与多值性
Skeleton series and multivaluedness of the self-energy functional in zero space-time dimensions
摘要：
最近，Kozik，Ferrero和Georges在数值上发现，对于一类相互作用费米子的基本模型，自能$Σ[G]$是完全修饰的单粒子传播子G的多值泛函，并且骨架图解级数$Σ_{\rm bold}[G]$在临界相互作用强度以上收敛到错误的分支.我们考虑零时空维的情况下，从初等代数出现相同的数学现象。我们也发现了一个类似的现象，完全大胆的形式主义建立在充分打扮的单粒子传播子和对传播子。
英文摘要：
Recently, Kozik, Ferrero and Georges have discovered numerically that for a family of fundamental models of interacting fermions, the self-energy $Σ[G]$ is a multi-valued functional of the fully dressed single-particle propagator G, and that the skeleton diagrammatic series $Σ_{\rm bold}[G]$ converges to the wrong branch above a critical interaction strength. We consider the zero space-time dimensional case, where the same mathematical phenomena appear from elementary algebra. We also find a similar phenomenology for the fully bold formalism built on fully dressed single-particle propagator and pair propagator.
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