Generalized variational principle for the time-dependent Hartree-Fock equations for a Slater determinant

The time-dependent Hartree-Fock equations are derived from a variational principle for the general N-body action of a Slater determinant of single-electron orbitals. The variational principle generalizes commonly used variational treatments based on reduced two-body actions. The self-consistent field equations are found to contain time-dependent corrections to the standard mean-field interactions. Their physical significance is discussed and a time-dependent phase shift to the Slater determinant is obtained that properly accounts for the total interaction energy in the mean-field approach.