{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T11:13:59Z","timestamp":1753874039704,"version":"3.41.2"},"reference-count":50,"publisher":"AIP Publishing","issue":"8","funder":[{"name":"CERN\/FP","award":["83505\/2008"],"award-info":[{"award-number":["83505\/2008"]}]}],"content-domain":{"domain":["pubs.aip.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2019,8,1]]},"abstract":"<jats:p>In this paper, we give an expression for canonical transformation group with Grassmann variables, basing on the Jacobi\u2009hsp \u2254 semidirect sum hN\u22casp(2N,R)C algebra of boson operators. We assume a mean-field Hamiltonian (MFH) linear in the Jacobi generators. We diagonalize the boson MFH. We show a new aspect of eigenvalues of the MFH. An excitation energy arisen from additional self-consistent field parameters has never been seen in the traditional boson mean-field theory. We derive this excitation energy. We extend the Killing potential in the Sp(2N,R)CU(N) coset space to the one in the Sp(2N+2,R)CU(N+1) coset space and make clear the geometrical structure of K\u00e4hler manifold, a non-compact symmetric space Sp(2N+2,R)CU(N+1). The Jacobi\u2009hsp transformation group is embedded into an Sp(2N+2,R)C group and an Sp(2N+2,R)CU(N+1) coset variable is introduced. Under such mathematical manipulations, extended bosonization of Sp(2N+2,R)C Lie operators, vacuum function and differential forms for extended boson are presented by using integral representation of boson state on the Sp(2N+2,R)CU(N+1) coset variables.<\/jats:p>","DOI":"10.1063\/1.5109944","type":"journal-article","created":{"date-parts":[[2019,8,27]],"date-time":"2019-08-27T12:12:58Z","timestamp":1566907978000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":1,"title":["Mean-field theory based on the Jacobi\u2009hsp\u2008\u2254 semidirect sum hN\u22casp(2N,R)C algebra of boson operators"],"prefix":"10.1063","volume":"60","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"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2614-7775","authenticated-orcid":false,"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":"317","published-online":{"date-parts":[[2019,8,27]]},"reference":[{"key":"2023073103544955600_c1","doi-asserted-by":"publisher","first-page":"1175","DOI":"10.1103\/physrev.108.1175","volume":"108","year":"1957","journal-title":"Phys. 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