Neutrino-assisted Fermion--Boson Transitions

Abstract

We study fermion-boson transitions. Our approach is based on the 3 × 3 subequations of Dirac and Duffin-Kemmer-Petiau equations, which link these equations. We demonstrate that free Dirac equation can be invertibly converted to spin-0 Duffin-Kemmer-Petiau equation in presence of a neutrino field. We also show that in special external fields, upon assuming again existence of a neutrino (Weyl) spinor, the Dirac equation can be transformed reversibly to spin-0 Duffin-Kemmer-Petiau equation. We argue that such boson-fermions transitions are consistent with the main channel of pion decay.

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.…”

“…We have demonstrated that, in the noninteracting case, full covariant solutions of the = 0 and = 1 DKP equations are generalized solutions of the same Dirac equation; see (1), (15), and (24). More exactly, if we choose the modified spinor representation of the Dirac matrices defined in (16) then the following functions Ψ = (, ) , A = (, 2×2 ) , and B = (, − ) with = are solutions of the same Dirac equation and correspond to = 1/2, = 0, and = 1 cases, respectively.…”

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

“…(1) we have π AḂ = σ 0 π 0 + − → σ · − → π AḂ , π µ = p µ − qA µ , σ k (k = 1, 2, 3) are the Pauli matrices, and σ 0 is the 2 × 2 unit matrix. Let us note that equations (1), (2), which can be written in the 7 × 7 Hagen-Hurley form, were first proposed by Dirac [20]. Equations (1) in explicit form read:…”

“…These wavefunctions are non-standard since they involve higher-order spinors. We have demonstrated recently that in the s = 0 case the generalized solutions describe decay of a pion [2]. The aim of this work is to interpret spin 1 solutions, possibly in the context of weakly decaying particles.…”

“…) are the Pauli matrices, and σ 0 is the 2 × 2 unit matrix. Let us note that equations (1), (2), which can be written in the 7 × 7 Hagen-Hurley form, were first proposed by Dirac [20].…”