Grassmann Numbers and Clifford-Jordan-Wigner Representation of Supersymmetry

被引：8

作者：

Catto, Sultan ^{[1
]}

Choun, Yoon S. ^{[1
,2
]}

Guercan, Yasemin

Khalfan, Amish ^{[3
,4
]}

Kurt, Levent ^{[1
]}

机构：

[1] CUNY, Grad Sch, Dept Phys, New York, NY 10010 USA

[2] Rockefeller Univ, New York, NY 10021 USA

[3] Manhattanville Coll, New York, NY 10577 USA

[4] Yeshiva Univ, New York, NY 10033 USA

来源：

XXTH INTERNATIONAL CONFERENCE ON INTEGRABLE SYSTEMS AND QUANTUM SYMMETRIES (ISQS-20) | 2013年 / 411卷

关键词：

D O I：

10.1088/1742-6596/411/1/012009

中图分类号：

O59 [应用物理学];

学科分类号：

摘要：

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.

引用

页数：19

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