Representationless Formalism in the Field Theory of Fixed Nucleons

Abstract

The usual approach to field theory, in which state vectors are expanded in terms eigenvectors ${H}_{0}$, 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 the renormalized coupling constant $f$ gives finite observables 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 the quotients two power series in $f$. The method is applied to the calculation 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 the moment, but the scalar part cannot be calculated on this model.