Rotation Symmetry and Nonabelian Berry Potential

Abstract

We study the role of rotational symmetry in the systems where nonabelian Berry potentials emerge as a result of integrating out fast degrees of freedom. The conserved angular momentum is constructed in the presence of a non-abelian Berry potential, which is formulated using Grassmann variables. The modifications on conventional angular momentum are discussed in close analogy with monopole systems. The diatomic molecular system discussed by Zygelman is found to have a similar structure to that of a non-abelian $SU(2)$ charge coupled to a 't Hooft - Polyakov monopole. The abelian limit of the Berry potential in diatomic systems is shown to be the same as $U(1)$ monopole and in a large separation limit, we observe the decoupling associated with a vanishing field tensor.