Connection Constraints from Non-Abelian Supersymmetric Quantum Mechanics

TL;DR

This paper explores how supersymmetry imposes non-abelian constraints on the Berry connection in quantum mechanics, revealing new structures like monopole behavior in the case of SU(2).

Contribution

It generalizes the constraints on the Berry connection to fields transforming under internal symmetry groups, uncovering novel non-abelian conditions.

Findings

Constraints lead to monopole-like behavior for SU(2)

Extension of supersymmetry constraints to non-abelian internal symmetries

New geometric structures in supersymmetric quantum mechanics

Abstract

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