Grassmann Numbers and Clifford-Jordan-Wigner Representation of Supersymmetry
Grassmann Numbers and Clifford-Jordan-Wigner Representation of Supersymmetry
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格拉斯曼数和超对称性的 Clifford-Jordan-Wigner 表示
DOI：
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发表时间：
2013
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通讯作者：
L. Kurt
中科院分区：
文献类型：
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作者：
S. Catto;Y. Choun;Y. Gürcan;A. Khalfan;L. Kurt
物理学中的基本粒子是根据相同粒子交换下的多粒子态的行为来分类的：玻色子态是对称的，而费米子态是反对称的。这也体现在各个创生算子的交换属性中：玻色子创生算子可交换，而费米子创生算子反交换。因此，使用交换实体（例如复数变量）来研究玻色子是很自然的，而为了描述费米子，反交换变量更自然地适合。在本文中，我们介绍了这些反交换且乍一看不熟悉的变量（格拉斯曼数）并研究了它们的属性。特别是，我们简要讨论了格拉斯曼数的微分和积分。部分工作由能源部合同号 DE-AC-0276-ER 03074 和 03075 支持； NSF 拨款号 DMS-8917754。
The elementary particles of Physics are classified according to the behavior of the multi-particle states under exchange of identical particles: bosonic states are symmetric while fermionic states are antisymmetric. This manifests itself also in the commutation properties of the respective creation operators: bosonic creation operators commute while fermionic ones anticommute. It is natural therefore to study bosons using commuting entities (e.g. complex variables), whereas to describe fermions, anticommuting variables are more naturally suited. In this paper we introduce these anticommuting- and at first sight unfamiliar- variables (Grassmann numbers) and investigate their properties. In particular, we briefly discuss differential and integral calculus on Grassmann numbers. Work supported in part by DOE contracts No. DE-AC-0276-ER 03074 and 03075; NSF Grant No. DMS-8917754.