On the Mechanism of Fermion-Boson Transformation

Abstract

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.

Neutrino-assisted Fermion--Boson Transitions

“…In the present paper we generalize results of [9] in two directions. Firstly, we generalize the fermion-boson transformation connecting solutions of free Dirac and spin-0 DKP equations in presence of Weyl spinor.…”

“…More on these ideas can be found in Refs. [1,2,3,4], see also [5,6,7,8] and [9]. It seems, however, that a broader and unifying picture is still missing.…”

“…Recently, the smooth and controlled evolution from a fermionic Bardeen-Cooper-Schrieffer (BCS) superfluid state to a molecular Bose-Einstein condensate (BEC) has been realized in ultracold Fermi gases [11]. On the other hand, we have shown recently that solutions of the Dirac equation can be transformed in the non-interacting case, assuming existence of a constant spinor, to solutions of the spin-0 Duffin-Kemmer-Petiau (DKP) equation and vice versa [9]. Possible analogy between BCS-BEC transition and our findings is motivation of our work.…”

“…Covariance of these equations was established in [13] while the problem of covariance of their solutions was solved, to some extent, in Ref. [9].…”

Synthesis of Relativistic Wave Equations: The Noninteracting Case

“…On the other hand, these solutions do not contain all spinor components and are thus noncovariant solutions of covariant equations. We studied this problem in [23,24]. In the present work, we show that, in the free case, full covariant solutions of the = 0 and = 1 DKP equations are generalized solutions of the Dirac equation.…”