1999/09/29 by Ts. Dankova, G. Rosensteel
Physics and Astronomy · #nucl-th
published as in Highlights of Modern Nuclear Structure: Proceedings of the 6th International Spring Seminar on Nuclear Physics, Ed. A. Covello, World-Scientific (1999) · 9 pages
arxiv created 1999/09/29 · arxiv updated 2009/12/01
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^∗ 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.