# Gamma 5 dirac matrice

1. Jun 9, 2010

### IRobot

Hi, i wonder somethin'

when I see that definition of the matrice:
$$\gamma^5=\gamma^0\gamma^1\gamma^2\gamma^3$$
I don't see why it is a pseudo-scalar.

2. Jun 9, 2010

### Rus Almighty

If you inspect $$\gamma^5$$,you can see that it anti commutes with $$\gamma^0$$ (while 0 stands for the time coordinate).
so under space inversion the expression will change it's sign
$$\psi^{\dag}\gamma^{0}\gamma^5\psi\rightarrow-\psi^{\dag}\gamma^0\gamma^5\psi$$
and that is a property of a Pseudoscalar

Last edited: Jun 9, 2010
3. Jun 11, 2010

### IRobot

Hum i see, thanks :).