Gauge theory of collective modes

G Rosensteel
2012 Journal of Physics, Conference Series  
The classical theory of Riemann ellipsoids is formulated naturally as a gauge theory based on a principal G-bundle P. The structure group G = SO(3) is the vorticity group, and the bundle P = GL+(3, R) is the connected component of the general linear group. The base manifold is the space of positive-definite real 3 × 3 symmetric matrices, identified geometrically with the space of inertia ellipsoids. Non-holonomic constraints determine connections on the bundle. In particular, the trivial
more » ... ion corresponds to rigid body motion, the natural Riemannian connection to irrotational flow, and the invariant connection to the falling cat. The curvature form determines the fluid's field tensor which is an analogue of the familiar Faraday tensor. Associated G-bundles and the covariant derivative yield new quantum geometrical collective models that are a natural generalization of the Bohr model. These new geometric structures formulate the collective model as a Yang-Mills gauge theory.
doi:10.1088/1742-6596/403/1/012010 fatcat:b3wdfmm4tzbd3hs7soaieezsjq