Theory of neutral particles: McLennan-Case construct for neutrino, its generalization, and a fundamentally new wave equation

Sep, 1994
19 pages
Published in:
  • Int.J.Mod.Phys.A 11 (1996) 1855-1874
e-Print:
Report number:
  • LA-UR-94-3118

Citations per year

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Abstract:
Continuing our recent argument where we constructed a FNBWW-type spin-11 boson having opposite relative intrinsic parity to that of the associated antiparticle, we now study eigenstates of the Charge Conjugation operator. Based on the observation that if ϕL(p μ)\phi_{_{L}}(p~\mu) transforms as a (0,j)(0,\,j) spinor under Lorentz boosts, then Θ[j]ϕL (p μ)\Theta_{[j]}\,\phi_{_{L}}~\ast(p~\mu) transforms as a (j,0)(j,\,0) spinor (with a similar relationship existing between ϕR(p μ)\phi_{_{R}}(p~\mu) and Θ[j]ϕR (p μ)\Theta_{[j]}\,\phi_{_{R}}~\ast(p~\mu); where Θ[j]JΘ[j] 1=J  \Theta_{[j]}\,{\bf J}\,\Theta_{[j]}~{-1}\,=\,-\,{\bf J}~\ast with Θ[j]\Theta_{[j]} the well known Wigner matrix involved in the operation of time reversal) we introduce McLennan-Case type (j,0)(0,j)(j,\,0)\oplus(0,\,j) spinors. Relative phases between ϕR(p μ)\phi_{_{R}}(p~\mu) and Θ[j]ϕR (p μ)\Theta_{[j]}\,\phi_{_{R}}~\ast(p~\mu), and Θ[j]ϕL (p μ)\Theta_{[j]}\,\phi_{_{L}}~\ast(p~\mu) and ϕL(p μ)\phi_{_{L}}(p~\mu), turn out to have physical significance and are fixed by appropriate requirements. Explicit construction, and a series of physically relevant properties, for these spinors are obtained for spin-1/21/2 and spin-11 culminating in the construction of a fundamentally new wave equation and introduction of Dirac-like and Majorana-like quantum fields.
  • neutrino: model
  • spinor
  • helicity
  • field equations
  • group theory: Lorentz
  • group theory: representation
  • charge conjugation
  • parity