Renormalization and Asymptotics
Renormalization and Asymptotics
复制标题
重正化和渐进
DOI：
10.1142/s0217979200001035
复制
发表时间：
2000
影响因子：
1.7
通讯作者：
Y. Oono
中科院分区：
文献类型：
--
作者：
Y. Oono
在对Stuckelberg-Petermann型（即场论）重整化群（RG）理论进行了简单的介绍之后，通过简单的例子解释了它在微分方程渐近行为研究中的应用。奇异摄动方法研究微分方程渐近行为的实质是将微分方程化为控制长时间尺度行为的方程（即约化摄动）。RG方法将约化方程作为RG方程给出（这称为约化重整化群方法）。RG方程一旦写出，就可以通过求解RG方程得到渐近性态，同时也便于渐近解的误差分析。通过本文中解释的“原RG方程”的新方法进一步简化了RG的还原使用。例如，对于最低的非平凡阶，该方法不需要任何显式计算的微扰结果。
After a gentle introduction to the Stuckelberg–Petermann style (i.e. field-theoretical) renormalization group (RG) theory, its application to the study of asymptotic behaviors of differential equations is explained through simple examples. The essence of singular perturbation methods to study asymptotic behaviors of differential equations is to reduce it to equations governing long time scale behaviors (i.e. the so-called reductive perturbation). The RG approach gives the reduced equation as an RG equation (this is called the reductive renormalization group approach). Once the RG equation is written down, the asymptotic behavior can be obtained by solving it. The RG equation also facilitates the error analysis of the asymptotic solutions. A new approach via "proto-RG equation" explained in this article further simplifies the reductive use of RG. For example, to the lowest nontrivial order the approach does not require any explicit calculation of perturbative results.