非常规最小减法和Bogoliubov-Parasyuk-Hepp-Zimmermann：质量标量理论和临界指数
Unconventional minimal subtraction and Bogoliubov-Parasyuk-Hepp-Zimmermann: massive scalar theory and critical exponents
摘要：
我们介绍了一个更简单的，但非常规的最小减法重整化过程的情况下，大量的标量$λϕ^{4}$理论在欧氏空间使用维正则化。我们表明，这种方法是非常相似的无质量场论中的对应物。特别是，选择使用裸露的质量在较高的微扰阶，而不是采用其树级对应消除了所有蝌蚪插入该命令。作为一个应用，我们图解计算临界指数$η$和$ν$至少两个循环。我们进行了明确的比较与Bogoliubov-Parasyuk-Hepp-Zimmermann（$BPHZ$）方法在相同的循环顺序，表明所提出的方法需要更少的图表，并建立两种方法之间的连接。
英文摘要：
We introduce a simpler although unconventional minimal subtraction renormalization procedure in the case of a massive scalar $λϕ^{4}$ theory in Euclidean space using dimensional regularization. We show that this method is very similar to its counterpart in massless field theory. In particular, the choice of using the bare mass at higher perturbative order instead of employing its tree-level counterpart eliminates all tadpole insertions at that order. As an application, we compute diagrammatically the critical exponents $η$ and $ν$ at least up to two loops. We perform an explicit comparison with the Bogoliubov-Parasyuk-Hepp-Zimmermann ($BPHZ$) method at the same loop order, show that the proposed method requires fewer diagrams and establish a connection between the two approaches.
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