Geometry of spin shape space
Presenting author: Edgar Guzmán-González
Given a spin j, we define the spin shape space as the quotient of the space of the spin space under the action of the rotation group SO(3). This permits us to decompose the spin space as a fiber bundle, where the base is shape space an the fiber is generically isomorphic to SO(3). Using the Fubini-Study metric, we can define a connection and a metric in the fibers and in shape space in a natural way. Here we will present some applications of this decomposition to quantum mechanics, particularly, to the Berry's curvature, along with some mathematical results of the induced geometry in spin shape space.