The Majorana representation of spins and the relation between $SU(\infty)$ and $SDiff(S^2)$
Abstract
The Majorana representation of spin$\frac{n}{2}$ quantum states by sets of points on a sphere allows a realization of SU(n) acting on such states, and thus a natural action on the twodimensional sphere $S^2$. This action is discussed in the context of the proposed connection between $SU(\infty)$ and the group $SDiff(S^2)$ of areapreserving diffeomorphisms of the sphere. There is no need to work with a special basis of the Lie algebra of SU(n), and there is a clear geometrical interpretation of the connection between the two groups. It is argued that they are {\it not} isomorphic, and comments are made concerning the validity of approximating groups of areapreserving diffeomorphisms by SU(n).
 Publication:

arXiv eprints
 Pub Date:
 April 2004
 arXiv:
 arXiv:hepth/0405004
 Bibcode:
 2004hep.th....5004S
 Keywords:

 High Energy Physics  Theory