SUPERSYMMETRY AND SUPERALGEBRA FOR THE 2-BODY SYSTEM WITH A DIRAC OSCILLATOR INTERACTION

Some years ago, one of the authors (MM) revived a concept to which he gave the name single-particle Dime oscillator, while another of the au thors (CQ) showed that it corresponds to a realization of supersymmetr ic quantum mechanics. The Dirac oscillator in its one- and many-body v ersions has had a great number of applications. Recently, it included the analytic expression for the eigenstates and eigenvalues of a two-p article system with a new type of Dirac oscillator interaction of freq uency omega. By considering the latter together with its partner corre sponding to the replacement of omega by -omega, we are able to get a s upersymmetric formulation of the problem and find the superalgebra tha t explains its degeneracy.