重正化群方法。III。微扰分析
A renormalisation group method. III. Perturbative analysis
摘要：
本文是一系列致力于发展一个严格的重整化群方法的格子场论涉及玻色子场，费米子场，或两者兼而有之。在本文中，我们激励和二阶微扰重整化的一般方法，并将其应用到一个特定的超对称场论，代表连续时间弱自避免行走$\mathbb{Z}^d$。我们的重点是关键维度$d=4$。结果包括推导的扰动流的耦合常数，与伴随的估计系数的流动。这些是必要的结果，随后应用到4维弱自回避行走，包括证明存在对数校正其临界标度。经过微小的修改，我们的结果也适用于4维$n$ -分量$|φ|^4$自旋模型.
英文摘要：
This paper is the third in a series devoted to the development of a rigorous renormalisation group method for lattice field theories involving boson fields, fermion fields, or both. In this paper, we motivate and present a general approach towards second-order perturbative renormalisation, and apply it to a specific supersymmetric field theory which represents the continuous-time weakly self-avoiding walk on $\mathbb{Z}^d$. Our focus is on the critical dimension $d=4$. The results include the derivation of the perturbative flow of the coupling constants, with accompanying estimates on the coefficients in the flow. These are essential results for subsequent application to the 4-dimensional weakly self-avoiding walk, including a proof of existence of logarithmic corrections to their critical scaling. With minor modifications, our results also apply to the 4-dimensional $n$-component $|φ|^4$ spin model.
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