Yang-Mills Theory for the Nuclear Collective Model

The primary goal of this discussion is to understand the dynamics of collective nuclear rotations. The main theoretical tool to achieve this goal is a gauge theory that uses a bundle connection. The bundle structure connects the angular and vortex degrees of freedom. The novel technique proposed for this research is the Yang-Mills theory of bundle connections. The character of nuclear rotations depends quantitatively on the connection between angular and vortex degrees of freedom. The Yang-Mills equation provides the correct equation for determining this connection. To this end, the underlying differential geometric relationship between Yang-Mills theory and the nuclear collective model will be discussed. Although similar mathematically, the underlying physics is substantially different. Minkowski space is the common base manifold for the Yang-Mills theories of electromagnetism and the electroweak forces; the corresponding gauge groups are U(1), SU(2)xU(1). The base manifold for the proposed Yang-Mills collective model is the space of nuclear rotations and quadrupole deformations; the gauge symmetry is SO(3), the group of vortex motions.