离壳超对称与滤Clifford超模
Off-shell supersymmetry and filtered Clifford supermodules
摘要：
超对称的离壳表示是超庞加莱代数在动态无约束场空间上的表示。我们正式描述这种表示，在领域和他们的时空衍生物，我们解释的物理概念的工程尺寸作为一个整体的分级。我们证明了一维N-扩展超对称的形式分次离壳表示，超庞加莱代数p^{1| N}，对应于Cl（N）上的滤Clifford超模。我们还证明了二维（p，q）-超对称的形式分次离壳表示，超Poincare代数p^{1，1| p，q}，对应于Cl（p+q）上的双滤Clifford超模.我们的主要工具是过滤超代数和超模的形式变形，它们给出了过滤空间和具有偶度移位注入的分次空间之间的一一对应。这推广了机器开发的Gerstenhaber证明，每一个过滤代数是一个变形的相关分次代数。我们的治疗扩展Gerstenhaber的讨论的情况下，过滤是兼容的超对称结构，以及过滤模块除了过滤代数。我们还描述了类似的结构的双过滤和bigrading。
英文摘要：
An off-shell representation of supersymmetry is a representation of the super Poincare algebra on a dynamically unconstrained space of fields. We describe such representations formally, in terms of the fields and their spacetime derivatives, and we interpret the physical concept of engineering dimension as an integral grading. We prove that formal graded off-shell representations of one-dimensional N-extended supersymmetry, i.e., the super Poincare algebra p^{1|N}, correspond to filtered Clifford supermodules over Cl(N). We also prove that formal graded off-shell representations of two-dimensional (p,q)-supersymmetry, i.e., the super Poincare algebra p^{1,1|p,q}, correspond to bifiltered Clifford supermodules over Cl(p+q). Our primary tools are the formal deformations of filtered superalgebras and supermodules, which give a one-to-one correspondence between filtered spaces and graded spaces with even degree-shifting injections. This generalizes the machinery developed by Gerstenhaber to prove that every filtered algebra is a deformation of its associated graded algebra. Our treatment extends Gerstenhaber's discussion to the case of filtrations which are compatible with a supersymmetric structure, as well as to filtered modules in addition to filtered algebras. We also describe the analogous constructions for bifiltrations and bigradings.
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