The Majorana representation of spins and the relation between $SU(\infty)$ and $SDiff(S^2)$

Details The Majorana representation of spins and the relation between $SU(\infty)$ and $SDiff(S^2)$ The Majorana representation of spins and the relation between $SU(\infty)$ and $SDiff(S^2)$

2004-04-30

arxiv.org/abs/hep-th/0405004v1

Physics

High Energy Physics

High Energy Physics - Theory

Scientific paper

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 two-dimensional sphere $S^2$. This action is discussed in the context of the proposed connection between $SU(\infty)$ and the group $SDiff(S^2)$ of area-preserving 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 area-preserving diffeomorphisms by SU(n).

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