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Lowering and Raising Operators for the Orthogonal Group in the Chain O(n) ⊃ O(n − 1) ⊃ … , and their Graphs

Pang, Sing Chin; Hecht, K. T.

Pang, Sing Chin; Hecht, K. T.

1967-06

Citation:Pang, Sing Chin; Hecht, K. T. (1967). "Lowering and Raising Operators for the Orthogonal Group in the Chain O(n) ⊃ O(n − 1) ⊃ … , and their Graphs." Journal of Mathematical Physics 8(6): 1233-1251. <http://hdl.handle.net/2027.42/70553>

Abstract: Normalized lowering and raising operators are constructed for the orthogonal group in the canonical group chain O(n) ⊃ O(n − 1) ⊃ … ⊃ O(2) with the aid of graphs which simplify their construction. By successive application of such lowering operators for O(n), O(n − 1), … on the highest weight states for each step of the chain, an explicit construction is given for the normalized basis vectors. To illustrate the usefulness of the construction, a derivation is given of the Gel'fand‐Zetlin matrix elements of the infinitesimal generators of O(n).