Title:

The soliton of the effective chiral action in the twopoint approximation

In this thesis, we study the "twopoint approximation" for highly nonlocal effective actions, in the particular case of the Chiral Soliton Model of the nucleon. The nucleon in this model is regarded as being made of three valence quarks bound together by a meson field in a soliton form. Mesons are treated in mean field theory and the vacuum energy due to onequark loops is included. The theory is defined with a finite cutoff in momentum space, consistent with an effective theory for the lowenergy description of the strong interactions. We use the twopoint approximation to calculate the vacuum correction to the chiral soliton energy for a variety of soliton profile functions, investigating the effect of different regularisation schemes. Results are little influenced by the choice of the cutoff, and are within 20% of exact calculations, done with the full inclusion of the Dirac sea. We then perform a dynamical calculation of the chiral soliton by including seaquark effects selfconsistently in the twopoint approximation. We find a typical 20% (or less) deviation in the soliton energy from exact calculations. We apply a further "pole" approximation which leads to a significant algebraic simplification in the selfconsistent equations. We show, in particular, that a simple numerical fit of the pole form to the twopoint cutoff function yields essentially indistinguishable results from the latter. We finally calculate some static nucleon observables in the twopoint approximation and find general agreement with exact calculations. In view of the results obtained, we may hope that the pole form of the twopoint approximation may prove to be a generally useful approach to similar problems involving highly nonlocal actions.
