论文标题
现场演算：没有Feynman图的量子和统计场理论
Field Calculus: Quantum and Statistical Field Theory without the Feynman Diagrams
论文作者
论文摘要
对于给定的基本空间$ m $（时空），我们考虑了Guichardet在$ m $上的guichardet空间。在这里，我们基于Guichardet积分来开发一个“字段演算”。这是描述玻色子系统绿色功能关系的自然环境。在这里，我们可以遵循Schwinger的建议，并开发一种差异（本地领域）方法，而不是Feynman率先进行的积分方法。这得到了DEFG（Dyson-Einstein-Feynman-Guichardet）速记的帮助，该速记极大地简化了表达方式。这为Schwinger和Tomonaga的正式方法提供了方便的框架，而不是Feynman图。戴森·辛金（Dyson-Schwinger）在玻色症创建/歼灭操作员的帮助下重铸了这种语言。我们还为树木扩张提供了组合方法。
For a given base space $M$ (spacetime), we consider the Guichardet space over the Guichardet space over $M$. Here we develop a ''field calculus'' based on the Guichardet integral. This is the natural setting in which to describe Green function relations for Boson systems. Here we can follow the suggestion of Schwinger and develop a differential (local field) approach rather than the integral one pioneered by Feynman. This is helped by a DEFG (Dyson-Einstein-Feynman-Guichardet) shorthand which greatly simplifies expressions. This gives a convenient framework for the formal approach of Schwinger and Tomonaga as opposed to Feynman diagrams. The Dyson-Schwinger is recast in this language with the help of bosonic creation/annihilation operators. We also give the combinatorial approach to tree-expansions.
