Dirac Spinor


by ChrisVer
Tags: dirac, spinor
ChrisVer
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#1
Feb4-14, 10:36 AM
P: 376
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?
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Bill_K
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#2
Feb4-14, 01:56 PM
Sci Advisor
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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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