We study subsolutions of the Dirac and Duffin-Kemmer-Petiau equations described in our earlier papers. It is shown that subsolutions of the Duffin-Kemmer-Petiau equations and those of the Dirac equation obey the same Dirac equation with some built-in projection operator. This covariant equation can be referred to as supersymmetric since it has bosonic as well as fermionic degrees of freedom.

Abstract:In the present paper we study subsolutions of the Dirac and Duffin-Kemmer-Petiau equations in the interacting case. It is shown that the Dirac equation in longitudinal external fields can be split into two covariant subequations (Dirac equations with built-in projection operators). Moreover, it is demonstrated that the Duffin-Kemmer-Petiau equations in crossed fields can be split into two 3 × 3 subequations. We show that all the subequations can be obtained via minimal coupling from the same 3 × 3 subequations which are thus a supersymmetric link between fermionic and bosonic degrees of freedom.

Dynamics of a ball moving in gravitational field and colliding with a moving table is considered. The motion of the limiter is assumed as periodic with piecewise constant velocity. It is assumed that the table moves up with a constant velocity and then goes down with another constant velocity. The Poincaré map describing evolution from an impact to the next impact is derived. Several classes of solutions are computed in analytical form.

We study a fermion-boson transformation. Our approach is based on the 3 × 3 equations which are subequations of both the Dirac and Duffin-Kemmer-Petiau equations and thus provide a link between these equations. We show that solutions of the free Dirac equation can be converted to solutions of spin-0 Duffin-Kemmer-Petiau equation and vice versa. Mechanism of this transition assumes existence of a constant spinor.

We study internal structure of the Duffin-Kemmer-Petiau equations for spin 0 and spin 1 mesons. We show that in the noninteracting case full covariant solutions of thes=0ands=1DKP equations are generalized solutions of the Dirac equation.