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I can define

[itex]\gamma^5=i\gamma^0\gamma^1\gamma^2\gamma^3[/itex]

I know that the four gamma matrices [itex]\gamma^i\:\:,\;i=0...3[/itex] are invariant under a Lorentz transformation. So I can say that also [itex]\gamma ^5[/itex] is invariant, because it is a product of invariant matrices.

But this equality holds:

[tex]\gamma ^5=\frac{i}{4!}\epsilon_{\mu\nu\rho\sigma}\gamma^{\mu}\gamma^{\nu}\gamma^{\rho}\gamma^{\sigma}[/tex]

and this expression is not invariant!!

So, is [itex]\gamma^5[/itex] invariant or isn't it?

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# Homework Help: Dirac gamma matrices

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