Equal-time relativistic two-body equations

Abstract

A systematic study of the equal-time Hamiltonian two-body differential equations is presented, for all combinations of spinless and Dirac particles. Components with 'mixed' indices are eliminated in a new way. A new radial variable r' is introduced which reduces the equations to simpler 'quasipotential equations' which in some cases have exact solutions. A nonzero total momentum and a constant magnetic field are also discussed.

Relativistic Symmetry Suppresses Quark Spin-Orbit Splitting

“…This one quark Dirac Hamiltonian follows from the two-body Bethe-Salpeter equation in the equal time approximation, the spectator (Gross) equation with a simple kernel, and a two quark Dirac equation, in the limit that M is large [17][18][19]. If the vector potential, V V ( r), is equal to the scalar potential plus a constant potential, U, which is independent of the spatial location of the light quark relative to the heavy one, i.e., V V ( r) = V S ( r) + U, then the Dirac Hamiltonian is invariant under a spin symmetry [20,21], [ H , Ŝi ] = 0, where the generators of that symmetry are given by,…”

Breit type equation for mesonic atoms

“…There is no unique approach to calculate relativistic corrections to level shifts of bound two-body systems [12,13,15]. We shall employ the technique of the Breit equation as it is particularly suited to include form-factors effects in a rather transparent way.…”

Hydrogenic atoms with spinless nucleus in a magnetic field

“…So expressed, the Diaolike form of the Klein-Dirac equation has analytical solutions to order a4 (Pilkuhn 1992, MeliC 1994.…”