UBC Theses and Dissertations
The dressing transformation and its application to a fermion-boson trilinear interaction Hearn, Deborah Jean
In this thesis, various fermion-boson strong interaction potentials are determined as functions of the basic fermion-boson trilinear vertex function. Working in Fock space, we note that the fermion-boson trilinear interaction does not explicitly involve physical particles. We develop a transformation, called the dressing transformation, which acts on the fundamental particle creators and annihilators. They are transformed into physical particle operators, and the invariance properties and commutation relations of the theory are preserved. A precise technique for perturbatively determining the dressing transformation is formulated, and is applied to some simple models in field theory. The dressing transformation makes explicit the physical particle interactions implicit in the original trilinear interaction. When applied to the nucleon-pion trilinear interaction, we find a nucleon mass renormalization, a nucleon-pion scattering term, and a nucleon-nucleon scattering term present in the second-order dressed Hamiltonian. Using the NN7C vertex function derived from the Cloudy Bag Model, the nucleon-nucleon coordinate space potential can be calculated. We discover that providing the two nucleons are separated by a distance greater than twice the bag radius, the potential between them is given by the one pion exchange potential modified in strength by a function of the bag radius.
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