1 research outputs found
Noncommutative geometry of angular momentum space U(su(2))
We study the standard angular momentum algebra as a noncommutative manifold . 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. We embed inside a
4D noncommutative spacetime which is the limit of q-Minkowski space
and show that has a natural quantum isometry group given by the
quantum double as a singular limit of the -Lorentz group. We
view as a collection of all fuzzy spheres taken together. We
also analyse the semiclassical limit via minimum uncertainty states
approximating classical positions in polar coordinates.Comment: Minor revision to add reference [11]. 37 pages late