论文标题
尼尔森身份的图表结构
Diagrammatic structures of the Nielsen identity
论文作者
论文摘要
$γ$功能或规格场理论的有效潜力应符合尼尔森的身份，这意味着随着我们移动量规术语，有效的电位如何发展。在本文中，依靠Abelian玩具模型，我们旨在用$ \ Overline {r}_ξ$ gauge以图表形式证明这种身份。基本思想是在将图表部分区分为$ξ$参数之后，找出鬼链，并将图的腰部缩小到点，以将散装部分和$ c $ - 零件分开。可以将计算推广到使用非亚伯群，多个希格和费米亚多重组以及有限温度案例实施的模型。受此启发的启发，我们还建议在重新亮相超级图时，可以根据雏菊环之间的连接来扣除一些无关紧要的术语，以使Nielsen身份适合任意$ \ hbar $订单。
The $Γ$-function, or the effective potential of a gauge field theory should comply with the Nielsen identity, which implies how the effective potential evolves as we shift the gauge-fixing term. In this paper, relying on an abelian toy model, we aim at proving this identity in a diagrammatic form with the $\overline{R}_ξ$ gauge. The basic idea is to find out the ghost chain after partially differentiating the diagram by the $ξ$ parameter, and shrink the waists of the diagram into points to separate the bulk-part and $C$-part of the diagrams. The calculations can be generalized to the models implemented with non-abelian groups, multiple Higgs and fermion multiplets, and to the finite temperature cases. Inspired by this, we also suggest that when resumming the super-daisy diagrams, one can deduct some irrelevant terms at the connections between the daisy ringlets to fit the Nielsen identity up to arbitrary $\hbar$ orders.
