利用背景场方法和截断正则化对具有四次相互作用的四维标量模型量子作用量进行三圈重整化
Three-loop renormalization of the quantum action for a four-dimensional scalar model with quartic interaction with the usage of the background field method and a cutoff regularization
AI总结：
本文用背景场方法和截断正则化研究四维实 $\phi^4$ 理论，完成三圈重整化并验证 $\mathcal{R}$ 操作，给出重整化常数与 $\beta$ 函数前三个系数。
摘要：
本文采用背景场方法，在一般表述下研究了四维实 $\phi^4$ 理论的量子作用量。在坐标表象中利用截断正则化完成了三圈重整化。文中还以若干独立的三圈图为例，讨论了非局域奇异贡献的缺失以及重整化 $\mathcal{R}$ 操作的正确性。给出了重整化常数和 $\beta$ 函数前三个系数的显式形式，并表明结果与此前已知结果一致。
英文摘要：
The paper studies the quantum action for the four-dimensional real $ϕ^4$-theory in the case of a general formulation using the background field method. The three-loop renormalization is performed with the usage of a cutoff regularization in the coordinate representation. The absence of non-local singular contributions and the correctness of the renormalization $\mathcal{R}$-operation on the example of separate three-loop diagrams are also discussed. The explicit form of the first three coefficients for the renormalization constants and for the $β$-function is presented. Consistency with previously known results is shown.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
