标题： 超几何与量子场论，或：什么是经典构型？ 显示英文标题

标题： Supergeometry and Quantum Field Theory, or: What is a Classical Configuration?

摘要： 我们讨论了与经典费米场的反对易性相关的概念困难，并认为具有此类场的模型的所有经典构型的“空间”应被描述为无穷维超流形 M。我们讨论了关于超流形的两种主要方法，并探讨了许多物理学家倾向于选择罗杰斯方法的原因，尽管贝雷京-科斯特-列伊特斯方法更为根本。我们发展了后一种方法的无穷维变体，并证明先前论文中考虑的经典构型上的泛函实际上就是 M 上的超函数。我们提出了一个适用于任何具有费米场的经典场模型的未来数学工作的计划。该计划的部分内容已在后续论文中实现。 显示英文摘要

摘要： We discuss of the conceptual difficulties connected with the anticommutativity of classical fermion fields, and we argue that the "space" of all classical configurations of a model with such fields should be described as an infinite-dimensional supermanifold M. We discuss the two main approaches to supermanifolds, and we examine the reasons why many physicists tend to prefer the Rogers approach although the Berezin-Kostant-Leites approach is the more fundamental one. We develop the infinite-dimensional variant of the latter, and we show that the functionals on classical configurations considered in a previous paper are nothing but superfunctions on M. We present a programme for future mathematical work, which applies to any classical field model with fermion fields. This programme is (partially) implemented in successor papers.