Noncommutative geometry of angular momentum space U(su(2))

We study the standard angular momentum algebra [x(i),x(j)]=ilambdaepsilon(ijk)x(k) as a noncommutative manifold R-lambda(3). We show that there is a natural 4D differential calculus and obtain its cohomology and Hodge * operator. We solve the spin 0 wave equation and some aspects of the Maxwell or electromagnetic theory including solutions for a uniform electric current density, and we find a natural Dirac operator partial derivative. We embed R-lambda(3) inside a 4D noncommutative space-time which is the limit q-->1 of q-Minkowski space and show that R-lambda(3) has a natural quantum isometry group given by the quantum double C(SU(2))xU(su(2)) which is a singular limit of the q-Lorentz group. We view R-lambda(3) as a collection of all fuzzy spheres taken together. We also analyze the semiclassical limit via minimum uncertainty states \j,theta,phi> approximating classical positions in polar coordinates. (C) 2003 American Institute of Physics.