Synthesis of Relativistic Wave Equations: The Noninteracting Case

Abstract

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.

Generalized Solutions of the Dirac Equation,WBosons, and Beta Decay

“…In the next Section we transform the Hagen-Hurley equations, in the interacting case, into two Dirac equations with non-standard solutions involving higher-order spinors, extending our earlier results described in [1]. These generalized solutions bear some analogy to generalized solutions of the Dirac equation argued to describe a lepton and three quarks [21].…”

“…Therefore, we shall base our theory on the 7 × 7 formulation, see Eqs. (18), (19) in [1] and Subsection 6 ii) in [19]. These equations violate parity P , where P :…”

“…Recently, we have shown that in the free case covariant solutions of the s = 0 and s = 1 Duffin-Kemmer-Petiau (DKP) equations are generalized solutions of the Dirac equation [1]. These wavefunctions are non-standard since they involve higher-order spinors.…”

“…Several classes of potentials were used in DKP equations to investigate interactions of spin 1 particles [6][7][8][9][10][11][12][13][14][15]. However, we shall apply the 7 × 7 Hagen-Hurley equations [16][17][18] in spinor form [1,19,20]. Our motivation stems from the observation that these equations violate parity and thus should describe weakly interacting particles.…”

“…We have shown recently that, in the non-interacting case, solutions of the s = 0 and s = 1 DKP equations are generalized solutions of the Dirac equation [1].…”