Relativistic wave equation for two dirac particles, suggested by the Duffin-Kemmer-Petiau algebra

Abstract

A new relativistic wave equation for two spin-1/2 particles is discussed which in the pointlike limit of tight bound states tends to the Duffin-Kemmer-Petiau equation for one spin-0 or spin-1 particle. The Bethe-Salpeter equation for two spin-1/2 particles can be rewritten in the new form. But, in the familiar case of an instantaneous interaction introduced through the minimal substitutionE→E−V of a «vector» potentialV, the new equation is neither equivalent to the Salpeter equation nor to the Breit equation. In particular, ifV is Coulombic atr→0, scalar states1S0 are (surprisingly) excluded from the new equation by the regularity condition atr=0, which may be a desirable feature in some composite models for W and Z bosons.