arXiv 2005.109002020-05hep-thcond-mat.stat-mech

有质量标量场论的类无质量最小减法

Masslesslike minimal subtraction for massive scalar field theory

Marcelo M. Leite

备注：: 5 pages, no figures, version accepted in Europhysics Letters
DOI：: 10.1209/0295-5075/ac335e

摘要：

本文介绍了具有$O(N)$内部对称性的有质量$λϕ^{4}$场论的最简单的最小减法，它类似于应用于无质量场的同样方法，只需要两个步骤。首先，在两点顶点部分的每个图中利用部分$p$操作，以便将其分别分离为具有不同系数的质量平方和外部动量的和。然后，使用{ \it参数解离变换}，作为二次质量系数的回路积分可以完全根据质量求解，不再依赖于外部动量。它包括在解决内部子图后，在剩余的循环积分中替换费曼参数的某个固定值的选择。我们检查的结果在图解计算的临界指数至少达到两个循环的顺序使用一个平坦的度量与欧几里德签名。

英文摘要：

We introduce the simplest minimal subtraction method for massive $λϕ^{4}$ field theory with $O(N)$ internal symmetry, which resembles the same method applied to massless fields by using two steps. First, the utilization of the partial-$p$ operation in every diagram of the two-point vertex part in order to separate it into a sum of squared mass and external momentum, respectively, with different coefficients. Then, the loop integral which is the coefficient of the quadratic mass can be solved entirely in terms of the mass, no longer depending upon the external momentum, using the {\it parametric dissociation transform}. It consists in the choice of a certain set of fixed values of Feynman parameters replaced inside the remaining loop integral after solving the internal subdiagrams. We check the results in the diagrammatic computation of critical exponents at least up to two-loop order using a flat metric with Euclidean signature.

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