论文标题
格拉斯曼尼亚随机分析和欧几里得费米斯的随机量化
Grassmannian stochastic analysis and the stochastic quantization of Euclidean Fermions
论文作者
论文摘要
我们介绍了用于用于欧几里得费米量量子场理论随机量化的Grassmann随机变量的随机分析。从量子概率的角度来看，有关Grassmann代数的分析：Grassmann随机变量是抽象的Grassmann代数的同态变量，即量子概率空间，即具有合适状态的A $ C^{\ ast} $ - 代数。我们定义了高斯过程的概念，布朗运动和随机（部分）微分方程，以格拉斯曼代数为代数。我们使用它们来研究有限和无限的尺寸Langevin Grassmann随机微分方程，由高斯时空白噪声驱动并描述其不变措施。作为一种应用，我们提供了随机量化的证明，以及去除尤卡伊卡瓦模型的空间截止。
We introduce a stochastic analysis of Grassmann random variables suitable for the stochastic quantization of Euclidean fermionic quantum field theories. Analysis on Grassmann algebras is developed here from the point of view of quantum probability: a Grassmann random variable is an homomorphism of an abstract Grassmann algebra into a quantum probability space, i.e. a $C^{\ast}$-algebra endowed with a suitable state. We define the notion of Gaussian processes, Brownian motion and stochastic (partial) differential equations taking values in Grassmann algebras. We use them to study the long time behavior of finite and infinite dimensional Langevin Grassmann stochastic differential equations driven by Gaussian space-time white noise and to describe their invariant measures. As an application we give a proof of the stochastic quantization and of the removal of the space cut-off for the Euclidean Yukawa model.
