Supersymmetric quantum mechanics and the index theorem
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.
scientific article; zbMATH DE number 436595
scientific article