This dissertation documents the results of two related efforts. Firstly, a model of nucleon-nucleon (NN) interactions is developed based on scalar field theory. Secondly, the relativistic 2-body Bethe-Salpeter equation (BSE) is generalized to handle inelastic processes in the ladder approximation. Scalar field theory describes the behavior of scalar particles, particles with spin 0. In the present work scalar field theory is used to describe NN interactions mediated by pion exchange. The scalar theory is applied to nucleons despite the fact that nucleons are fermions, spin 1/2 particles best described by fourcomponent Dirac spinor fields. Nevertheless, the scalar theory is shown to give a good fit to experiment for the total cross sections for several reactions . The results are consistent with more elaborate spinor models involving one boson exchange (OBE). The results indicate that the spin and isospin of nucleons can to some extent be ignored under certain conditions. Being able to ignore spin and isospin greatly reduces the complexity of the model. A limitation of the scalar theory is that it does not distinguish between particle and anti-particle. Consequently one must decide how to interpret the s-channel diagrams generated by the theory, diagrams which involve particle creation and annihilation. The issue is resolved by extending the scalar theory to include electric charge, and formulating NN interactions in terms of complex scalar fields, which are able to describe both particles and anti-particles. A generalized Bethe-Salpeter equation (GBSE) is developed to handle inelastic processes in the ladder approximation. The GBSE, formulated using the scalar theory, is new, and introduces a systematic method for analyzing families of coupled reactions. A formalism is developed centered around the amplitude matrix M' defined for a given Lagrangian. M' gives the amplitudes of a family of reactions that arise from the Lagrangian. The formalism demonstrates how these amplitudes, to 2nd order, segregate into independent groups of coupled BSE's. The GBSE formalism is applied to the coupled BSE (CBSE) of Faassen and Tjon (FT)  for the reaction N+N->N+Delta, showing that the CBSE is missing a coupling channel, and in the expansion, under counts ladder diagrams. A proof is given of the equivalence of the series of ladder diagrams generated by M' and the S-matrix. A section on future work discusses several projects for further development and application of the GBSE.
Worcester Polytechnic Institute
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Dick, F. A. (2007). Scalar Field Theories of Nucleon Interactions. Retrieved from https://digitalcommons.wpi.edu/etd-dissertations/165
ladder approximation, inelastic process, Bethe-Salpeter, BSE, pion, nucleon, scalar field, Scalar field theory, Nucleon-nucleon interactions, Bethe-Salpeter equation