The Symmetric Group and the Gel'fand Basis of U(3). Generalizations of the Dirac Identity
- 1 September 1972
- journal article
- research article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 13 (9) , 1389-1393
- https://doi.org/10.1063/1.1666151
Abstract
It is shown that the symmetrization of N particle states by means of the orthogonal units of the algebra of the symmetric group SN yields the Gel'fand basis states of the irreducible representations of U(3). The existence of generalizations of the Dirac identity is demonstrated, and a connection between the symmetrized two‐ and three‐body exchange operators and the invariants of U(3) is established.Keywords
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