In this Rapid Communication, we show analytically that all pure entangled states of two d-dimensional systems (qudits) violate the Collins-Gisin-Linden-Masser-Popoescu (CGLMP) inequality. Thus one has the Gisins theorem for two qudits.
We show that the relativistic hydrogen atom possesses an SO(4) symmetry by introducing a kind of pseudo-spin vector operator. The same SO(4) symmetry is still preserved in the relativistic quantum system in presence of an U(1) monopolar vector potent
ial as well as a nonabelian vector potential. Lamb shift and SO(4) symmetry breaking are also discussed.
