This regulator is gauge invariant in an abelian theory due to the auxiliary particles being minimally coupled to the photon field through the gauge covariant derivative. It is not gauge covariant in a non-abelian theory, though, so Pauli–Villars regularization is more difficult to use in QCD calculations. P–V serves as a helpful alternative to the more commonly used dimensional regularization in specific circumstances, such as in chiral phenomena, where a change of dimension alters the properties of the Dirac gamma matrices.