MS4格式中$β$ -函数的有限无Z积分表达式
Finite Z-less integral expressions for $β$-functions in the MS4 scheme
摘要：
紫外重整化的广义最小减法方案（Kuznetsov和Tkachov，1988）是根据应用情况进行微调的。由此产生的$\text{MS}^4$计划避免无关的正则化，并使动量积分减去麻烦的渐近项在物理上正确的方式，由于使用特殊的最小减法算子定义一致的物理自然的Polchinski截止。Callan-Symanzik方程的直接推导避免了发散的重整化因子或反项，并自动产生重整化群函数的显式精确有限积分表达式。
英文摘要：
The generalized minimal subtraction scheme for ultraviolet renormalization (Kuznetsov and Tkachov, 1988) is fine-tuned with applications in mind. The resulting $\text{MS}^4$ scheme obviates extraneous regularizations and renders momentum integrands integrable by subtracting troublesome asymptotic terms in a physically correct fashion due to the use of special minimal subtraction operators defined congruously with the physically natural Polchinski cutoffs. A direct derivation of the Callan-Symanzik equations avoids divergent renormalization factors or counterterms, and automatically yields explicit exact finite integral expressions for renormalization group functions.
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