ISSN:
1089-7658
Source:
AIP Digital Archive
Topics:
Mathematics
,
Physics
Notes:
In this paper the reports on collectivity and geometry are concluded, where the microscopic description of many-body collective motions and their relation with the symplectic geometry of the n-particle system are reexamined. In the present paper it is shown that, modulo linear canonical transformations, the symplectic algebra sp(6,R) admits only three maximal subalgebras sp(2,R)⊕o(3), u(3), and cm(3), which contain the rotation algebra o(3). The objective is to discuss the spectra and shapes of "pure'' many-body systems for which the Hamiltonian is associated with a Casimir operator up to the second degree in the generators of a given maximal subalgebra, as well as those of "transitional'' systems, where the Hamiltonian is a function of the generators and Casimir operators of several of the maximal subalgebras.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.528342
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