# Dirac Spinor

by ChrisVer
Tags: dirac, spinor
 P: 292 Hello. I would like to ask something that will help me understand a little better how we work with Dirac spinors' inputs.... I know that the dirac equation has 4 independent solutions, and for motionless particles, the (spinor) solutions are: $u_{+}=(1,0,0,0)^{T}$ electron +1/2 $u_{-}=(0,1,0,0)^{T}$ electron -1/2 $v_{+}=(0,0,1,0)^{T}$ positron +1/2 $v_{-}=(0,0,0,1)^{T}$ positron -1/2 Now suppose that I write a solution as: $Ψ=(1,0,0,1)^{Τ}$ Does that mean that I'm having 2 particles (one positron and one electron) involved?
 Sci Advisor P: 3,697 In the single-particle first quantized theory, the four components of the spinor represent particle states with spin ±ħ/2 and energy ±E. So just as ψ = (1,1,0,0) represents a state with equal probability of the particle having spin up and down, so ψ = (1,0,0,1) represents a state with equal probability of the particle having spin up energy +E, and spin down energy -E. In the framework of this theory there is no antiparticle.

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