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Noninvariance groups in the second-quantization picture and their applications

par Moshinsky, Marcos;Quesne, Christiane
Référence Journal of mathematical physics, 11, 5, page (1631-1639)
Publication Publié, 1970

Article révisé par les pairs

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Résumé :

We investigate the existence of noninvariance groups in the second-quantization picture for fermions distributed in a finite number of states. The case of identical fermions in a single shell of angular momentum j is treated in detail. We show that the largest noninvariance group is a unitary group U(22j+1). The explicit form of its generators is given both in the m scheme and in the seniority-angular-momentum basis. The full set of 0-, 1-, 2-, ⋯, (2j + 1)-particle states in they shell is shown to generate a basis for the single irreducible representation [1] of U(22j+1). The notion of complementary subgroups within a given irreducible representation of a larger group is defined, and the complementary groups of all the groups commonly used in classifying the states in the j shell are derived within the irreducible representation [1] of U(22j+1). These concepts are applied to the treatment of many-body forces, the state-labeling problem, and the quasiparticle picture. Finally, the generalization to more complex configurations is briefly discussed.