论文标题
亚临界欧几里得菲尔米管田理论的随机分析
A stochastic analysis of subcritical Euclidean fermionic field theories
论文作者
论文摘要
在先前关于格拉斯曼随机变量随机分析的工作的基础上，我们引入了前向后的随机微分方程（FBSDE），该方程提供了格拉斯曼措施的随机定量。我们的方法的灵感来自所谓的连续重量级化组，但避免了直接研究流动方程的技术困难。作为一种应用，我们构建了一个弱耦合的亚临界欧几里得式菲尔米米因田间理论的家族，并证明了相关性的指数衰减。
Building on previous work on the stochastic analysis for Grassmann random variables, we introduce a forward-backward stochastic differential equation (FBSDE) which provides a stochastic quantisation of Grassmann measures. Our method is inspired by the so-called continuous renormalisation group, but avoids the technical difficulties encountered in the direct study of the flow equation for the effective potentials. As an application, we construct a family of weakly coupled subcritical Euclidean fermionic field theories and prove exponential decay of correlations.
