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NILPOTENT ELEMENTS IN PHYSICS

机译:物理中的万能元素

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We briefly review some issues of the nilpotent objects in theoretical physics using simple models as an illustration. Nilpotent elements appear at quantum and classical level in several ways. On the one hand there are celebrated BRST operators, external derivative and related with them cohomology theory, on the other hand there are dual numbers which are a less known structure than complex numbers but important in many approaches, then there are commuting nilpotent variables, somehow generalizing the nilpotent but anticommuting Grassmann variables used in super-mathematics and SUSY models. As an interesting fact we note that nilpotent variables demand the use of the generalized light-cone geometry with the metric of the null signature.
机译:我们以简单的模型为例,简要回顾了理论物理学中幂等物体的一些问题。幂等元素以几种方式出现在量子和经典水平。一方面有著名的BRST算子,外部导数以及与它们的同调理论相关,另一方面,有对偶数,其结构比复数少,但在许多方法中都很重要,然后对换能指数变量进行某种方式的交换推广了超数学和SUSY模型中使用的幂等但反换向的Grassmann变量。作为一个有趣的事实,我们注意到幂等变量要求使用具有空签名度量的广义光锥几何体。

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