Self-Consistent-Field Method and $τ$-Functional Method on Group Manifold in Soliton Theory: a Review and New Results

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dc.creatorNishiyama, Seiya
dc.creatorda Providencia, Joao
dc.creatorProvidencia, Constanca
dc.creatorCordeiro, Flavio
dc.creatorKomatsu, Takao
dc.date2009-01-22
dc.date.accessioned2026-07-07T12:32:58Z
dc.date.available2026-07-07T12:32:58Z
dc.descriptionThe maximally-decoupled method has been considered as a theory to apply an basic idea of an integrability condition to certain multiple parametrized symmetries. The method is regarded as a mathematical tool to describe a symmetry of a collective submanifold in which a canonicity condition makes the collective variables to be an orthogonal coordinate-system. For this aim we adopt a concept of curvature unfamiliar in the conventional time-dependent (TD) self-consistent field (SCF) theory. Our basic idea lies in the introduction of a sort of Lagrange manner familiar to fluid dynamics to describe a collective coordinate-system. This manner enables us to take a one-form which is linearly composed of a TD SCF Hamiltonian and infinitesimal generators induced by collective variable differentials of a canonical transformation on a group. The integrability condition of the system read the curvature C=0. Our method is constructed manifesting itself the structure of the group under consideration. >...
dc.identifierhttps://arxiv.org/abs/0901.3473
dc.identifierhttp://arxiv.org/abs/0901.3473
dc.identifierSIGMA 5 (2009), 009, 76 pages
dc.identifierdoi:10.3842/SIGMA.2009.009
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/216965
dc.subjectExactly Solvable and Integrable Systems
dc.subjectStatistical Mechanics
dc.subjectMathematical Physics
dc.subjectQuantum Physics
dc.titleSelf-Consistent-Field Method and $τ$-Functional Method on Group Manifold in Soliton Theory: a Review and New Results
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