论文标题
$φ^4_3 $度量的摄动理论，用霍普夫代数重新审视
Perturbation theory for the $Φ^4_3$ measure, revisited with Hopf algebras
论文作者
论文摘要
我们给出了一个相对较短的，几乎是独立的证据，证明了适当重新拟合的$φ^4_3 $测量的划分函数允许渐近扩张，而随着紫外线截止值的消除，其系数会汇聚。我们还研究了渐近系列的Borel总结性问题。这些证明基于Wiener混乱的扩展，Hopf代数方法以及通过BPHZ重态化获得的Feynman图的值。
We give a relatively short, almost self-contained proof of the fact that the partition function of the suitably renormalised $Φ^4_3$ measure admits an asymptotic expansion, the coefficients of which converge as the ultraviolet cut-off is removed. We also examine the question of Borel summability of the asymptotic series. The proofs are based on Wiener chaos expansions, Hopf-algebraic methods, and bounds on the value of Feynman diagrams obtained through BPHZ renormalisation.
