Gamma5 x d^2 Lorentz invariant?

1. Nov 4, 2011

cbetanco

is $\overline{\Psi}$ γ5 $\partial$2 $\Psi$ Lorentz Invariant? How does this term transform under Lorentz transformations? Here $\Psi$ is a Dirac field.

Thanks

2. Nov 4, 2011

clem

It transforms as a pseudoscalar.

3. Nov 4, 2011

cbetanco

So it changes as a scalar with respect to Lorentz transformations, but changes sign under parity? This means it is Lorentz invariant?

4. Nov 4, 2011

clem

The parity transformation is a Lorentz transformation, so you would have to say it is invariant under Lorentz transformations which do not include r --> -r.