Solving renormalization group equations with the Lambert W function
Solving renormalization group equations with the Lambert W function
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使用 Lambert W 函数求解重整化群方程
DOI：
10.1103/physrevd.87.085023
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发表时间：
2013
影响因子：
5
通讯作者：
Hidenori Sonoda
中科院分区：
文献类型：
--
作者：
山田泰一;(船木靖郎,明孝之,堀内昶,池田清美;G. Roepke;P. Schuck;東崎昭弘);J. Kubo;Hidenori Sonoda
一段时间以来，人们已经知道，一个无量纲参数的2圈重整化群方程可以在朗伯函数的封闭形式中求解。我们应用该方法的一般理论与高斯不动点，以构建重整化群不变的物理参数，如耦合常数和物理平方质量。作为进一步的应用，我们推测了四维线性σ模型的一个可能的精确有效势。
It has been known for some time that 2-loop renormalization group equations of a dimensionless parameter can be solved in a closed form in terms of the Lambertfunction. We apply the method to a generic theory with a Gaussian fixed point to construct renormalization group invariant physical parameters such as a coupling constant and a physical squared mass. As a further application, we speculate a possible exact effective potential for thelinear sigma model in four dimensions.