论文标题
运算符产品扩展和两环凝胶曼尼 - 低功能的计算
Operator Product Expansion and Calculation of the Two-Loop Gell-Mann-Low Function
论文作者
论文摘要
这项工作于1985年进行。它在Yad的俄罗斯人出版。 fiz。 44，498（1986）[英文翻译Sov。 J. Nucl。物理。 44，321（1986）]。这些出版物都没有在线可用。将本文提交给Arxiv将使其可访问。 ***开发了一种简单的方法，即可确定$β$功能的$ K $ - 环系数，如果已知$（k -1）$ loop中某些极化运算符的操作员产品扩展。 Gell-Mann-low函数的两环系数的计算变得微不足道 - 它减少到已经知道的表达式上的一些代数操作。作为例子，考虑了旋转器，标量和超对称电动力学。尽管在文献中已知$β^{（2）} $的各个结果，但计算方法和与操作员产品扩展有关的某些点都是新的。
This work was carried out in 1985. It was published in Russian in Yad. Fiz. 44, 498 (1986) [English translation Sov. J. Nucl. Phys. 44, 321 (1986)]. None of these publications are available on-line. Submitting this paper to ArXiv will make it accessible. *** A simple method is developed that makes it possible to determine the $k$-loop coefficient of the $β$-function if the operator product expansion for certain polarization operators in the $(k -1)$ loop is known. The calculation of the two-loop coefficient of the Gell-Mann-Low function becomes trivial -- it reduces to a few algebraic operations on already known expressions. As examples, spinor, scalar, and supersymmetric electrodynamics are considered. Although the respective results for $β^{(2)}$ are known in the literature, both the method of calculation and certain points pertaining to the construction of the operator product expansion are new.
