Point symmetries in the Hartree-Fock approach: Densities, shapes and currents

Three mutually perpendicular symmetry axes of the second order, inversion, and time reversal can be used to construct a double point group denoted by D2h(TD). Properties of this group are analyzed in relation to the symmetry and symmetry-breaking effects within the mean-field (Hartree-Fock) theories, both in even and odd fermion systems. We enumerate space symmetries of local one-body densities, and symmetries of electromagnetic moments, that appear when some or all of the D2h(TD) elements represent self-consistent mean-field symmetries.