- #1
ChrisVer
Gold Member
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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?
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?