Positronium on null-plane and Melosh transformation

The null-plane dynamics of positronium-like systems is studied in a quasipotential approach, in approximations depending on c, the velocity of light, being large. Neglecting terms in the quasi- potential of order c/sup -3/ (relative to particle rest energy) symmetries appear whose generators are analogous to the good null- plane charges of relativistic SU(6) hadron classification schemes. These symmetries are broken by terms of order c/sup -3/, which can, however, be transformed away by an appropriate approximation to the Melosh transformations. There then emerge better symmetries, broken only at order c/sup -4/. When both internal and overall velocities of a composite system are small of first order, and terms of second and higher order are neglected, these better symmetries coincide with those that appear in a Foldy-Wouthuysen description when spin-orbit coupling is neglected. (7 refs).