{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,1]],"date-time":"2022-04-01T12:04:35Z","timestamp":1648814675251},"reference-count":33,"publisher":"World Scientific Pub Co Pte Lt","issue":"10","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Mod. Phys. A"],"published-print":{"date-parts":[[2012,4,20]]},"abstract":"<jats:p> -1 The boson images of fermion SO(2N+1) Lie operators have been given together with those of SO(2N+2) ones. The SO(2N+1) Lie operators are generators of rotation in the (2N+1)-dimensional Euclidean space (N: number of single-particle states of the fermions). The images of fermion annihilation\u2013creation operators must satisfy the canonical anticommutation relations, when they operate on a spinor subspace. In the regular representation space we use a boson Hamiltonian with Lagrange multipliers to select out the spinor subspace. Based on these facts, a new description of a fermionic SO(2N+2) top is proposed. From the Heisenberg equations of motions for the boson operators, we get the SO(2N+1) self-consistent field (SCF) Hartree\u2013Bogoliubov (HB) equation for the classical stationary motion of the fermion top. Decomposing an SO(2N+1) matrix into matrices describing paired and unpaired modes of fermions, we obtain a new form of the SO(2N+1) SCF equation with respect to the paired-mode amplitudes. To demonstrate the effectiveness of the new description based on the bosonization theory, the extended HB eigenvalue equation is applied to a superconducting toy-model which consists of a particle\u2013hole plus BCS-type interaction. It is solved to reach an interesting and exciting solution which is not found in the traditional HB eigenvalue equation due to the unpaired-made effects. To complete the new description, the Lagrange multipliers must be determined in the classical limit. For this aim a quasi-anticommutation relation approximation is proposed. Only if a certain relation between an SO(2N+1) parameter z and the N is satisfied, unknown parameters K and l in the Lagrange multipliers can be determined without any inconsistency. <\/jats:p>","DOI":"10.1142\/s0217751x12500546","type":"journal-article","created":{"date-parts":[[2012,4,18]],"date-time":"2012-04-18T01:44:03Z","timestamp":1334713443000},"page":"1250054","source":"Crossref","is-referenced-by-count":2,"title":["A NEW DESCRIPTION OF MOTION OF THE FERMIONIC <i>SO<\/i>(2<i>N<\/i>+2) TOP IN THE CLASSICAL LIMIT UNDER THE QUASI-ANTICOMMUTATION RELATION APPROXIMATION"],"prefix":"10.1142","volume":"27","author":[{"given":"SEIYA","family":"NISHIYAMA","sequence":"first","affiliation":[{"name":"Centro de F\u00edsica Computacional, Departamento de F\u00edsica, Universidade de Coimbra, P-3004-516 Coimbra, Portugal"}]},{"given":"JO\u00c3O","family":"DA PROVID\u00caNCIA","sequence":"additional","affiliation":[{"name":"Centro de F\u00edsica Computacional, Departamento de F\u00edsica, Universidade de Coimbra, P-3004-516 Coimbra, Portugal"}]},{"given":"CONSTAN\u00c7A","family":"PROVID\u00caNCIA","sequence":"additional","affiliation":[{"name":"Centro de F\u00edsica Computacional, Departamento de F\u00edsica, Universidade de Coimbra, P-3004-516 Coimbra, Portugal"}]}],"member":"219","published-online":{"date-parts":[[2012,5,2]]},"reference":[{"key":"rf1","first-page":"41","volume":"7","author":"Bogoliubov N. 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