Key points are not available for this paper at this time.
The general method for constructing invariant phenomenological Lagrangians is described. The fields are assumed to transform according to (nonlinear) realizations of an internal symmetry group, given in standard form. The construction proceeds through the introduction of covariant derivatives, which are standard forms for the field gradients. The case of gauge fields is also discussed.
Callan et al. (Sat,) studied this question.