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UBC Theses and Dissertations

The dressing transformation and scattering of dressed particles in a model of fermions and bosons James, Howard Nelson


This thesis reviews a method in quantum field theory to yield models dealing explicitly with physical particle operators. The method involves a unitary transformation known as a dressing transformation which transforms the original particle creators into dressed physical particle creators. A dressing transformation is applied to a system of fermions and. bosons interacting via a trilinear Hamiltonian similar to the one found in The Cloudy Bag Model. The model is then specialized to describe systems of physical N-particles ('nucleons' without spin and isospin) and physical π-particles ('pions' without isospin). Our model is shown to describe the set of possible interactions involving N and π-particles including π-particle production and annihilation. In considering elastic Nπ scattering, an expression for the T-operator is derived when the incident free particles have a total energy near the energy of a Δ-particle. Equations for a two N-particle bound state, the d-particle ('deuteron') are given and using a set of modified Faddeev equations, we study the reactions occurring within the three channels NN, NN and πd.

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