# Dirac Spinor

1. Feb 4, 2014

### ChrisVer

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?

2. Feb 4, 2014

### Bill_K

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.