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 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).
- Publication:
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arXiv e-prints
- Pub Date:
- April 2004
- DOI:
- 10.48550/arXiv.hep-th/0405004
- arXiv:
- arXiv:hep-th/0405004
- Bibcode:
- 2004hep.th....5004S
- Keywords:
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- High Energy Physics - Theory