How similar are the spin states and the matter/antimatter states?
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Within the Dirac formalism, we have bispinors that represent both if a particle is spin up or spin down, and if a particle is an electron or a positron.
And these representations are very similar. (Along the z axis).
ψelectron,up=⎡⎣⎢⎢⎢1000⎤⎦⎥⎥⎥ψelectron,up=[1000], ψelectron,down=⎡⎣⎢⎢⎢0100⎤⎦⎥⎥⎥ψelectron,down=[0100]
ψpositron,up=⎡⎣⎢⎢⎢0010⎤⎦⎥⎥⎥ψpositron,up=[0010], ψpositron,up=⎡⎣⎢⎢⎢0001⎤⎦⎥⎥⎥ψpositron,up=[0001]
How close is the analogy between these two kinds of states? What properties of spin have a counterpart in the matter/antimatter state?
And these representations are very similar. (Along the z axis).
ψelectron,up=⎡⎣⎢⎢⎢1000⎤⎦⎥⎥⎥ψelectron,up=[1000], ψelectron,down=⎡⎣⎢⎢⎢0100⎤⎦⎥⎥⎥ψelectron,down=[0100]
ψpositron,up=⎡⎣⎢⎢⎢0010⎤⎦⎥⎥⎥ψpositron,up=[0010], ψpositron,up=⎡⎣⎢⎢⎢0001⎤⎦⎥⎥⎥ψpositron,up=[0001]
How close is the analogy between these two kinds of states? What properties of spin have a counterpart in the matter/antimatter state?
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