Supersymmetric quantum mechanics and the index theorem
type: Item
instance of: scholarly article
title: Supersymmetric quantum mechanics and the index theorem
zbMATH Open document ID: 0784.58064
DOI: 10.1016/0393-0440(93)90077-R
published in: Journal of Geometry and Physics
publication date: 1994-03-27T00:00:00Z
review text: The supersymmetric quantum mechanics describing a spinning particle that moves in a \(d\)-dimensional space-time is considered. The action for a relativistic point particle with spin 1/2 is written and then the quantization is realized in the standard way. The index theorem for the Dirac operator is extended to take into account the effect of anti- symmetric Abelian tensor fields. Then, the interactions with non-Abelian anti-symmetric tensor fields are investigated. It is shown that in both cases these fields do not give any nontrivial contributions to the Witten index. This means that if one couples a Dirac fermion to gravity or to non-Abelian gauge fields and non-Abelian anti-symmetric tensor fields, then no extra contributions to the axial anomaly will be found.
reviewed by: Gheorghe Zet
Mathematics Subject Classification ID: 58Z05
Mathematics Subject Classification ID: 83C47
Mathematics Subject Classification ID: 81Q60
Mathematics Subject Classification ID: 57R22
zbMATH DE Number: 436595
zbMATH Keywords: index theorem
zbMATH Keywords: supersymmetric quantum mechanics
zbMATH Keywords: spinning particle
author: R. H. Rietdijk
MaRDI profile type: Publication
cites work: Classical and quantum mechanics of a spinning particle interacting with background fields
cites work: Classical and quantum mechanics of a spinning particle interacting with anti-symmetric nonabelian tensor fields
cites work: Symmetries and motions in manifolds
cites work: Q3492324
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description: scientific article; zbMATH DE number 436595