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Reduction of the unitary group to its orthogonal or symplectic subgroup: A unified approach based upon complementary groups

par Quesne, Christiane
Référence Journal of Physics A: General Physics, 18, 14, page (2675-2684), 018
Publication Publié, 1985

Article révisé par les pairs

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Résumé :

A unified analysis of the state labelling problems for the d-row irreducible representations of U(n), when reduced with respect to either its orthogonal subgroup O(n) or its sympletic subgroup USp(n) (the latter in the even-n case), is carried out by using appropriate metrics and the complementarity relationship between the group O(n) and Sp(2d, R), or USp(n) and SO*(2d). In this way, a recently proposed canonical solution to the U(n) contains/implies O(n) state labelling problem is extended to the U(n) contains/implies USp(n) chain. This shows the equivalence between both these internal state labelling problems and the external state labelling problem for U(d), as expressed in Littlewood's branching rules for U(n) contains/implies O(n) and U(n) contains/implies USp(n).