Perturbative Correction to Transverse Ward-Takahashi Relation for the Vector Vertex

We re-derive exactly the transverse Ward–Takahashi relation for the vector vertex in momentum space. The result shows that this transverse Ward–Takahashi relation in momentum space involves a perturbative correction term. We demonstrate explicitly that this transverse Ward–Takahashi relation is satisfied indeed at one-loop order.

有向路上的保向部分一一变换半群

设In是集Xn={1,2,3,…,n}上的对称逆半群,且有向路为ρ={(1,2),(2,3),(3,4),…,(n-1,n)},令Iρ={α∈In:x,y∈dom,α(x,y)∈ρ■(xα,yα)∈ρ}∪{φ}.证明了Iρ是一个类A子半群,研究了Iρ的Green*-关系,进一步得到Ip的*理想.

一类富足半群的结构

利用左正则带和L*-幂单半群,给出了具有S-恰当断面的富足半群的一个结构定理.

Some Characterizations of Cryptogroups

In this paper, we give some characterizations of（regular, normal） cryptogroups with Green＇s relations, left（right） translations and homomorphisms.