dorsal/arxiv
View SchemaAlgebraic mean field theory
| Authors | Ts. Dankova, G. Rosensteel |
|---|---|
| Categories | |
| ArXiv ID | nucl-th/9909072 |
| URL | https://arxiv.org/abs/nucl-th/9909072 |
| Journal | in Highlights of Modern Nuclear Structure: Proceedings of the 6th International Spring Seminar on Nuclear Physics, Ed. A. Covello, World-Scientific (1999) |
Abstract
Mean field theory has an unexpected group theoretic mathematical foundation. Instead of representation theory which applies to most group theoretic quantum models, Hartree-Fock and Hartree-Fock-Bogoliubov have been formulated in terms of coadjoint orbits for the groups U(n) and O(2n). The general theory of mean fields is formulated for any arbitrary Lie algebra {\textbf g} of fermion operators. The moment map provides the correspondence between the Hilbert space of microscopic wave functions and the dual space {\textbf g}$^\ast$ of densities. The coadjoint orbits of the group in the dual space are phase spaces on which time-dependent mean field theory is equivalent to a classical Hamiltonian dynamical system. Indeed it forms a finite-dimensional Lax system. The SU(3) mean field theory is constructed explicitly in the coadjoint orbit framework.
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"abstract": "Mean field theory has an unexpected group theoretic mathematical foundation.\nInstead of representation theory which applies to most group theoretic quantum\nmodels, Hartree-Fock and Hartree-Fock-Bogoliubov have been formulated in terms\nof coadjoint orbits for the groups U(n) and O(2n). The general theory of mean\nfields is formulated for any arbitrary Lie algebra {\\textbf g} of fermion\noperators. The moment map provides the correspondence between the Hilbert space\nof microscopic wave functions and the dual space {\\textbf g}$^\\ast$ of\ndensities. The coadjoint orbits of the group in the dual space are phase spaces\non which time-dependent mean field theory is equivalent to a classical\nHamiltonian dynamical system. Indeed it forms a finite-dimensional Lax system.\nThe SU(3) mean field theory is constructed explicitly in the coadjoint orbit\nframework.",
"arxiv_id": "nucl-th/9909072",
"authors": [
"Ts. Dankova",
"G. Rosensteel"
],
"categories": [
"nucl-th"
],
"journal_ref": "in Highlights of Modern Nuclear Structure: Proceedings of the 6th\n International Spring Seminar on Nuclear Physics, Ed. A. Covello,\n World-Scientific (1999)",
"title": "Algebraic mean field theory",
"url": "https://arxiv.org/abs/nucl-th/9909072"
},
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