Equivalence Theorems for Meson-Nucleon Couplings

Abstract

The equivalence of pseudoscalar and pseudovector couplings of a pseudoscalar meson field with a nucleon field is examined. It is found that to the second order in the coupling constants the two couplings are equivalent except for two terms. One of these extra terms is predominantly an additional self-energy. The other occurs only for charged mesons and modifies the electromagnetic properties of a meson-nucleon system and the scattering of charged mesons. To this order (${g}^{2}$) it does not contribute to nuclear forces, Similarly, it is shown that the vector coupling of scalar mesons to nucleons can be replaced (to ${g}^{2}$) by a term identical with the last of the above-mentioned terms. These results show that the delta-function interactions which have been found in the past are actually not present.