The usual approach to field theory, in which state vectors are expanded in terms of eigenvectors of H0, is known to be inconsistent for point particles. An alternative method, in which only quantities bilinear in physical state vectors are considered, avoids this inconsistency. For the simplest case, the fixed point nucleon interacting with scalar charge-symmetric mesons, meaningful equations without infinite renormalization constants are obtained, and expansion in terms of the renormalized coupling constant f gives finite observables of one type. Observables "of the second kind," such as the interaction energy with an external field, cannot be defined as power series in f, but as limits of the quotients of two power series in f. The method is applied to the calculation of the magnetic nucleon moment in the static cutoff model with pseudovector coupling. Third and fifth approximations are calculated, and satisfactory convergence seems to prevail. The results are in agreement with experiments for the vector part of the moment, but the scalar part cannot be calculated on this model.