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Thanks!

- Thread starter copernicus1
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- #1

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Thanks!

- #2

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- #3

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(If your question is about the number of components and the fact that really gamma-mu is just a single matrix, then what the authors mean is that the second quantity transforms as a *component* of a four-vector.)

- #4

Bill_K

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In addition to transforming the spacetime coordinates, the Lorentz transformation also transforms the spinor components: ψ → Λψ, where Λ is a 4 x 4 matrix. For an infinitesimal transformation, Λ = I + ½ε_{μν}Σ^{μν} where Σ^{μν} = ½γ^{μ}γ^{ν}. It's their commutators with Σ^{μν} that determine the transformation properties of the Dirac covariants. For example, γ^{μ} → Λ^{-1}γ^{μ}Λ = γ'^{μ}.

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- #5

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For that you will have to learn how dirac spinors transform under parity.Under parity transformationAren't gamma-5 and gamma-mu just different matrices? How do you get a vector out of the second operation?

ψ

which shows that it has a pseudoscalar character.while ψ

ψ

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