Relations between different approaches to the relativistic two-body problem

On connection between the two-body Dirac oscillator and Kemmer oscillators

“…Let us investigate connections of (1) and (3) with the two-body Dirac oscillator [6][7][8] that we write in the form …”

“…Its modern treatment was proposed by Moshinsky and Sczcepaniak [2]; it has stimulated a lot of investigations connected with symmetries [3], supersymmetries (SUSY) [4,5], possible generalizations to the cases of multiparticle systems [6][7][8], and particles of higher spins [9][10][11][12]. In particular, let us mention that the spin-one equations with oscillatorlike potentials [9] admit a relatively new kind of symmetry called parasupersymmetry (PSUSY) [13,14].…”

Parasupersymmetries and Non-Lie Constants of Motion for Two-Particle Equations

“…11 Of course it is interesting to investigate physical and mathematical models which admit this new type of symmetry. It happens that a number of relatively recently proposed equations (connected with two-body [13][14][15][16] and one-body [18][19][20] problems) have a PSUSY nature and, moreover, there exist interesting connections between them.…”

“…In the present paper, we investigate symmetries and parasupersymmetries of relativistic two-particle equations with oscillator-equivalent potentials proposed by Moshinsky with collaborators. [13][14][15][16] These equations appear as two-body extensions of Dirac oscillator, 17 and, like the last, have a very rich symmetry structure.…”

“…We also analyze connections between two-body equations, [13][14][15][16] pararelativistic quantum oscillator equations 18,19 and the Kemmer oscillator equation. 20 Moreover, we propose a new Kemmer oscillator equation and two-particle equations for arbitrary spin particle with oscillator-equivalent potential.…”