{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,3]],"date-time":"2022-04-03T21:44:37Z","timestamp":1649022277444},"reference-count":30,"publisher":"World Scientific Pub Co Pte Lt","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Geom. Methods Mod. Phys."],"published-print":{"date-parts":[[2016,4]]},"abstract":"<jats:p> In a slight different way from the previous one, we propose a modified non-Euclidean transformation on the [Formula: see text] Grassmannian which gives the projected [Formula: see text] Tamm\u2013Dancoff equation. We derive a classical time-dependent (TD) [Formula: see text] Lagrangian which, through the Euler\u2013Lagrange equation of motion for [Formula: see text] coset variables, brings another form of the previous extended-TD Hartree\u2013Bogoliubov (HB) equation. The [Formula: see text] random phase approximation (RPA) is derived using Dyson representation for paired and unpaired operators. In the [Formula: see text] HB case, one boson and two boson excited states are realized. We, however, stress non-existence of a higher RPA vacuum. An integrable system is given by a geometrical concept of zero-curvature, i.e. integrability condition of connection on the corresponding Lie group. From the group theoretical viewpoint, we show the existence of a symplectic two-form [Formula: see text]. <\/jats:p>","DOI":"10.1142\/s0219887816500432","type":"journal-article","created":{"date-parts":[[2016,1,14]],"date-time":"2016-01-14T16:50:12Z","timestamp":1452790212000},"page":"1650043","source":"Crossref","is-referenced-by-count":0,"title":["Modified non-Euclidean transformation on the SO(2N+2) U(N+1) Grassmannian and SO(2N + 1) random phase approximation for unified description of Bose and Fermi type collective excitations"],"prefix":"10.1142","volume":"13","author":[{"given":"Seiya","family":"Nishiyama","sequence":"first","affiliation":[{"name":"Centro de F\u00edsica, Departamento de F\u00edsica, Universidade de Coimbra, P-3004-516 Coimbra, Portugal"}]},{"given":"Jo\u00e3o","family":"da Provid\u00eancia","sequence":"additional","affiliation":[{"name":"Centro de F\u00edsica, Departamento de F\u00edsica, Universidade de Coimbra, P-3004-516 Coimbra, Portugal"}]}],"member":"219","published-online":{"date-parts":[[2016,3,31]]},"reference":[{"key":"S0219887816500432BIB001","doi-asserted-by":"publisher","DOI":"10.1070\/PU1959v002n02ABEH003122"},{"key":"S0219887816500432BIB002","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRev.108.1175"},{"key":"S0219887816500432BIB003","doi-asserted-by":"publisher","DOI":"10.1143\/PTP.66.348"},{"key":"S0219887816500432BIB004","doi-asserted-by":"publisher","DOI":"10.1143\/PTP.57.1554"},{"key":"S0219887816500432BIB005","unstructured":"J. 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