论文标题
在随机PDES中重新归一化的微局部方法
A Microlocal Approach to Renormalization in Stochastic PDEs
论文作者
论文摘要
我们提出了一个新的框架，用于研究大量非线性随机PDE，这是受量子场理论的代数方法的启发。主要优点是，通过在功能值分布的合适代数内实现随机字段，我们能够使用适当的微局部分析技术，使我们能够讨论重新归化及其相关的自由度，而无需诉诸于任何正则化方案以及无限量的亚收集。作为方法的有效性，我们将其应用于随机$φ^3_d $模型的扰动分析。
We present a novel framework for the study of a large class of non-linear stochastic PDEs, which is inspired by the algebraic approach to quantum field theory. The main merit is that, by realizing random fields within a suitable algebra of functional-valued distributions, we are able to use techniques proper of microlocal analysis which allow us to discuss renormalization and its associated freedomw without resorting to any regularization scheme and to the subtraction of infinities. As an example of the effectiveness of the approach we apply it to the perturbative analysis of the stochastic $Φ^3_d$ model.
