- #1
eoghan
- 207
- 7
Hi!
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?
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?