Subtractions in Dispersion Relations
Subtractions in Dispersion Relations
复制标题
色散关系中的减法
DOI：
10.1103/physrev.123.1895
复制
发表时间：
1961
期刊：
影响因子：
--
通讯作者：
A. Kanazawa
中科院分区：
文献类型：
--
作者：
M. Sugawara;A. Kanazawa
证明了如下定理：如果解析函数f（z）只在真实的轴上有奇点，并且在无穷远处的大小由z的有限但任意的幂有界，则f（z）在无穷远处处处有本质上相同的极限。这个定理使人们能够用f（z）在无穷远处的边界值来表示柯西围道积分的无限圆的贡献，该边界值沿着仅一条延伸到无穷远处的割线。由此确定了精确的色散关系。作为例子，我们推导了前向和双π介子-核子色散关系，假设总截面在无限能量下接近有限极限。我们看到减法是如何完全由定理决定的。
The following theorem is proved: If an analytic function f (z) has singularities only on the real axis and is bounded in magnitude at infinity by a finite but arbitrary power of z, then f (z) has essentially the same limits everywhere at infinity. This theorem enables one to express the contribution from the infinite circle of the Cauchy contour integral in terms of the boundary values of f (z) at infinity along only one of the cuts extending to infinity. The exact dispersion relation is thus determined. As examples, we derive the forward and double pion-nucleon dispersion relations, assuming that the total cross section approaches a finite limit at infinite energy. We see how the subtractions are determined completely by the theorem.