Berezin integration of functions of anticommuting Grassmann variables is usually seen as a formal operation, sometimes even defined via differentiation. Using the formalism of geometric algebra and geometric calculus in which the Grassmann numbers are endowed with a second associative product coming from a Clifford algebra structure, we show how Berezin integrals can be realized in the high dimensional limit as integrals in the sense of geometric calculus. We then show how the concepts of spinors and superspace transform into this framework.

中文翻译：

---

作为黎曼和的别列津积分

反对易格拉斯曼变量函数的别列津积分通常被视为形式运算，有时甚至通过微分定义。使用几何代数和几何微积分的形式主义，其中格拉斯曼数被赋予了来自 Clifford 代数结构的第二个结合积，我们展示了如何在高维极限下将 Berezin 积分实现为几何微积分意义上的积分。然后我们展示了旋量和超空间的概念如何转化为这个框架。