Yang-Mills generalization of the geometrical collective model

The geometrical or Bohr-Mottelson model is generalized and recast as a Yang-Mills theory. The gauge symmetry determines conservation of Kelvin circulation. The circulation commutes with the Hamiltonian when it is the sum of the kinetic energy and a potential that depends only on deformation. The conventional Bohr-Mottelson model is the special case of circulation zero, and wave functions are complex-valued. In the generalization, any quantized value of the circulation is allowed, and the wave functions are vector-valued. The Yang-Mills formulation introduces a new coupling between the geometrical and intrinsic degrees of freedom. The coupling appears in the covariant derivative term of the collective kinetic energy. This kind of coupling is sometimes called ``magnetic" because of the analogy with electrodynamics.