Algebraic mean field theory

Details Algebraic mean field theory Algebraic mean field theory

1999-09-29

arxiv.org/abs/nucl-th/9909072v1

in Highlights of Modern Nuclear Structure: Proceedings of the 6th International Spring Seminar on Nuclear Physics, Ed. A. Cove

Physics

Nuclear Physics

Nuclear Theory

9 pages

Scientific paper

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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