{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T10:49:22Z","timestamp":1753872562462,"version":"3.41.2"},"reference-count":50,"publisher":"AIP Publishing","issue":"5","content-domain":{"domain":["pubs.aip.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2007,5,1]]},"abstract":"<jats:p>To go beyond perturbative method in terms of variables of collective motion, using infinite-dimensional fermions, we have aimed to construct the self-consistent-field (SCF) theory, i.e., time dependent Hartree-Fock theory on associative affine Kac-Moody algebras along the soliton theory. In this paper, toward such an ultimate goal we will reconstruct a theoretical frame for a \u03c5 (external parameter)-dependent SCF method to describe more precisely the dynamics on the infinite-dimensional fermion Fock space. An infinite-dimensional fermion operator is introduced through Laurent expansion of finite-dimensional fermion operators with respect to degrees of freedom of the fermions related to a \u03c5-dependent and a \u03a5-periodic potential. As an illustration, we derive explicit expressions for the Laurent coefficients of soliton solutions for sl\u0302n and for su\u0302n on infinite-dimensional Grassmannian. The associative affine Kac-Moody algebras play a crucial role to determine the dynamics on the infinite-dimensional fermion Fock space.<\/jats:p>","DOI":"10.1063\/1.2734864","type":"journal-article","created":{"date-parts":[[2007,5,4]],"date-time":"2007-05-04T17:46:27Z","timestamp":1178300787000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":0,"title":["Self-consistent-field method and \u03c4-functional method on group manifold in soliton theory. II. Laurent coefficients of soliton solutions for sl\u0302n and for su\u0302n"],"prefix":"10.1063","volume":"48","author":[{"given":"Seiya","family":"Nishiyama","sequence":"first","affiliation":[{"name":"Universidade de Coimbra Centro de F\u00edsica Te\u00f3rica, , 3000-Coimbra, Portugal"}]},{"given":"Jo\u00e3o","family":"da Provid\u00eancia","sequence":"additional","affiliation":[{"name":"Universidade de Coimbra Centro de F\u00edsica Te\u00f3rica, , 3000-Coimbra, Portugal"}]},{"given":"Takao","family":"Komatsu","sequence":"additional","affiliation":[{"name":"Universidade de Coimbra Centro de F\u00edsica Te\u00f3rica, , 3000-Coimbra, Portugal"}]}],"member":"317","published-online":{"date-parts":[[2007,5,3]]},"reference":[{"first-page":"381","volume-title":"Proceedings of the Sixth International Wigner Symposium","year":"2002","key":"2023070522580457700_c1"},{"volume-title":"The Nuclear Many-Body Problem","year":"1980","key":"2023070522580457700_c2"},{"key":"2023070522580457700_c3","doi-asserted-by":"publisher","first-page":"955","DOI":"10.1002\/qua.560200502","volume":"20","year":"1981","journal-title":"Int. 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