Please use this identifier to cite or link to this item:
https://hdl.handle.net/10316/110420
DC Field | Value | Language |
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dc.contributor.author | Nishiyama, Seiya | - |
dc.contributor.author | Providencia, João da | - |
dc.contributor.author | Providência, Constança | - |
dc.contributor.author | Cordeiro, Flávio | - |
dc.contributor.author | Komatsu, Takao | - |
dc.date.accessioned | 2023-11-22T12:30:04Z | - |
dc.date.available | 2023-11-22T12:30:04Z | - |
dc.date.issued | 2009-01-22 | - |
dc.identifier.issn | 18150659 | pt |
dc.identifier.uri | https://hdl.handle.net/10316/110420 | - |
dc.description.abstract | The 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. To go beyond the maximaly-decoupled method, we have aimed to construct an SCF theory, i.e., (external parameter)-dependent Hartree–Fock (HF) theory. Toward such an ultimate goal, the -HF theory has been reconstructed on an affine Kac–Moody algebra along the soliton theory, using infinite-dimensional fermion. An infinite-dimensional fermion operator is introduced through a Laurent expansion of finite-dimensional fermion operators with respect to degrees of freedom of the fermions related to a -dependent potential with a -periodicity. A bilinear equation for the -HF theory has been transcribed onto the corresponding -function using the regular representation for the group and the Schur-polynomials. The -HF SCF theory on an infinite-dimensional Fock space F1 leads to a dynamics on an infinite-dimensional Grassmannian Gr1 and may describe more precisely such a dynamics on the group manifold. A finite-dimensional Grassmannian is identified with a Gr1 which is affiliated with the group manifold obtained by reducting gl(1) to sl(N) and su(N). As an illustration we will study an infinite-dimensional matrix model extended from the finite-dimensional su(2) Lipkin–Meshkov–Glick model which is a famous exactly-solvable model. | pt |
dc.language.iso | eng | pt |
dc.publisher | Department of Applied Research, Institute of Mathematics of National Academy of Science of Ukraine | pt |
dc.relation | POCTI/FIS/451/94 | pt |
dc.relation | PTDC/FIS/64707/2006 | pt |
dc.relation | CERN/FP/83505/2008 | pt |
dc.rights | openAccess | pt |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-sa/4.0/ | pt |
dc.subject | self-consistent field theory | pt |
dc.subject | collective theory | pt |
dc.subject | soliton theory | pt |
dc.subject | affine KM algebra | pt |
dc.title | Self-Consistent-Field Method and $τ$-Functional Method on Group Manifold in Soliton Theory: a Review and New Results | pt |
dc.type | article | - |
degois.publication.firstPage | 009 | pt |
degois.publication.title | Symmetry, Integrability and Geometry: Methods and Applications (SIGMA) | pt |
dc.peerreviewed | yes | pt |
dc.identifier.doi | 10.3842/SIGMA.2009.009 | pt |
degois.publication.volume | 5 | pt |
dc.date.embargo | 2009-01-22 | * |
uc.date.periodoEmbargo | 0 | pt |
item.grantfulltext | open | - |
item.cerifentitytype | Publications | - |
item.languageiso639-1 | en | - |
item.openairetype | article | - |
item.openairecristype | http://purl.org/coar/resource_type/c_18cf | - |
item.fulltext | Com Texto completo | - |
crisitem.author.researchunit | CFisUC – Center for Physics of the University of Coimbra | - |
crisitem.author.orcid | 0000-0003-4215-3067 | - |
crisitem.author.orcid | 0000-0001-6464-8023 | - |
Appears in Collections: | FCTUC Física - Artigos em Revistas Internacionais |
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