Hj. Kull et D. Pfirsch, Generalized variational principle for the time-dependent Hartree-Fock equations for a Slater determinant, PHYS REV E, 61(5), 2000, pp. 5940-5947
The time-dependent Hartree-Fock equations are derived from a variational pr
inciple for the general N-body action of a Slater determinant of single-ele
ctron orbitals. The variational principle generalizes commonly used variati
onal treatments based on reduced two-body actions. The self-consistent fiel
d equations are found to contain time-dependent corrections to the standard
mean-field interactions. Their physical significance is discussed and a ti
me-dependent phase shift to the Slater determinant is obtained that properl
y accounts for the total interaction energy in the mean-field approach.