Lagrangian, scalar or pseudo-scalar?

[salparadise]

Hi,

My question is. Can in principle, a Lagrangian density for some theory be a pseudo-scalar. Normally people say that the Lagrangian needs to be a scalar, but it case it is a pseudo-scalar it would also be a eigaen function of the parity operator.

This topic could well be on the classical physics section, but as this is more relevant in quantum theory I decided to place it here.

Thanks

 

[dextercioby]

The normal requirement is that the fields transform irreducibly under the spacetime symmetry group and that the lagrangian density is a scalar under the spacetime symmetry group. The symmetry requirement for QFT in Minkowski spacetime is restricted Poincare group plus CPT plus gauge invariance. The Lagrangian density should be a scalar wrt to the 3 altogether or each taken separately.