Browsing by Author "Takyi, Ishmael"
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- ItemCollective coordinate description of kink-antikink interaction(Stellenbosch : Stellenbosch University, 2015-12) Takyi, Ishmael; Weigel, Herbert; Stellenbosch University. Faculty of Science. Dept. of Physics.ENGLISH ABSTRACT: In this thesis we explore resonance solutions in one space and one time dimensions in the nonlinear non-integrable ø⁴ and ø⁶ models. These resonances occur when the relative velocity between the kink and antikink falls below a specific critical velocity. It has been claimed that the presence of an internal vibrational mode is a necessary condition for the existence of these solutions. However, this mode is part of the solutions in the small amplitude formulation only in the ø⁴ model. Based on this, we investigate whether the availability of such a mode in the (reduced) collective coordinate ansätze will explain the resonance solutions regardless of whether or not it is a solution within the small amplitude approximation. We extend previous collective coordinate ansätze to three independent functions. Except for special scenarios this circumvents the problem seen in earlier studies that the coordinates are ill-declined when the kink-antikink separation tends to zero. We quantitatively compare the numerical results of the ordinary differential equations obtained from these ansätze to that of the partial differential equations in both the ø⁴ and ø⁶ models.
- ItemStructure functions of the nucleon in a soliton model(Stellenbosch : Stellenbosch University, 2019-04) Takyi, Ishmael; Weigel, Herbert; Scholtz, Frederik G.; Stellenbosch University. Faculty of Science. Dept. of Physics.ENGLISH ABSTRACT : We study nucleon structure functions (both polarized and unpolarized functions) within the Nambu-Jona-Lasinio (NJL) model, in which the nucleons emerge as solitons. In particular we investigate the polarized vacuum contribution to the nucleon structure functions. Rather than copying the quark distribution interpretation from QCD, we start from a fully regularized action functional to establish an intrinsically consistent formulation of the structure functions. For that matter we will employ the Pauli-Villars subtraction scheme to incorporate the vacuum polarization effects within the bosonized NJL model. Using Cutkosky’s rules the structure functions are extracted from the imaginary part of the Compton tensor. The structure functions are then evaluated numerically which includes a perturbative DGLAP evolution calculation before comparing our results with empirical data.