Gamma5 x d^2 Lorentz invariant?

[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

 

[Meir Achuz]

It transforms as a pseudoscalar.

 

[cbetanco]

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

 

[Meir Achuz]

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.