标题： 非（反）交换超空间、贝克-坎贝尔-豪斯多夫闭合形式和狄拉克-凯勒扭曲超对称性 显示英文标题

标题： Non(anti)Commutative Superspace, Baker-Campbell-Hausdorff Closed Forms, and Dirac-Kähler Twisted Supersymmetry

摘要： 从与非（反）交换Grassmann参数相关的超李群元素的初等计算开始，我们推导出若干Baker-Campbell-Hausdorff (BCH) 公式的闭合表达式，这些公式表示了相应超空间中超李群元素的乘法性质。 然后我们表明，由于存在非（反）交换性，超空间的参数化可能变得无限维。 我们证明了一种具有特定类型变形的Dirac-Kähler 扭转超对称（SUSY）代数（也称为Marcus B型扭转超对称代数或几何Langlands扭转超对称代数），我们称之为指数变形，可以绕过这个问题。 我们还通过超对称代数的规范协变化提供了指数变形的几何理解，并发现本文构建的框架可以作为非（反）交换超空间框架，提供扭曲超杨-米尔斯理论在格点上的规范协变链接形式。 显示英文摘要

摘要： Starting from an elementary calculation of super Lie group elements associating with non(anti)-commutative Grassmann parameters, we derive several closed expressions of Baker-Campbell-Hausdorff (BCH) formula which represent multiplication properties of super Lie group elements in the corresponding superspace. We then show that parametrization of superspace in general may become infinite dimensional due to the presence of non(anti)commutativity. We show that a Dirac-K\"ahler Twisted SUSY Algebra (also referred to as Marcus B-type Twisted SUSY Algebra or Geometric Langlands Twisted SUSY Algebra) with a certain type of deformation, which we call an exponential deformation, may circumvent this problem. We also provide, in terms of gauge covariantization of the SUSY algebra, a geometric understanding of the exponential deformation, and see that the framework constructed in this paper may serve as a non(anti)commutative superspace framework providing the gauge covariant link formulation of twisted super Yang-Mills on a lattice.