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Dirac Spinor 
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#1
Feb414, 10:36 AM

P: 736

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: [itex] u_{+}=(1,0,0,0)^{T} [/itex] electron +1/2 [itex] u_{}=(0,1,0,0)^{T} [/itex] electron 1/2 [itex] v_{+}=(0,0,1,0)^{T} [/itex] positron +1/2 [itex] v_{}=(0,0,0,1)^{T} [/itex] positron 1/2 Now suppose that I write a solution as: [itex] Ψ=(1,0,0,1)^{Τ}[/itex] Does that mean that I'm having 2 particles (one positron and one electron) involved? 


#2
Feb414, 01:56 PM

Sci Advisor
Thanks
P: 4,160

In the singleparticle 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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