Connection Constraints from Non-Abelian Super symmetric QuantumMechanics

[摘要] We generalise the study of constraints imposed by supersymmetry on the Berry connection to transformations with component elds in representations of an internal symmetry group G. Since the elds act as co-ordinates of the underlying space one nds a non-trivial extension to its structure and, correspondingly, there are new non-abelian constraints on the Berry connection. The speci c case of G = SU(2) is shown to constrain the connection to behave as a magnetic monopole over su(2), its Lie algebra.