Complex sine-Gordon theory: solitons, defects and boundaries

Abstract

This thesis presents research into the properties and features of the complex sine- Gordon theory. The CSG theory is a dimensional integrable held theory that admits soliton solutions which carry a Noether charge due to the U(I) invariance of the theory. Integrable CSG defects and boundaries are constructed and interactions between solitons, defects and boundaries are analysed at the classical and quantum level. The introduction of defects into the theory is facilitated by a new Backlund transformation involving two parameters. Defect conditions, constructed so they maintain the integrability of the theory and found to be exactly the BT, are used to sew two CSG theories together. How solitons interact with the defect is investigated, in particular whether as in the SG theory solitons can be absorbed and emitted by the defect. The classical time-delay and phase-shift are calculated for soliton-defect and particle-defect scattering. Using the CSG defect to dress the Dirichlet boundary a new CSG boundary theory is produced. Its integrability is checked by the explicit construction of conserved charges. The various interactions between solitons and the boundary are analysed, compared and contrasted with the defect theory. Finally aspects of the quantum CSG boundary theory are examined, culminating in a conjecture for the quantum reflection matrix for a Q = -1-1 soliton reflecting from an unexcited boundary. Reflection and boundary bootstrap procedures are used to generate the general reflection matrix for any charged soliton reflecting from any excited boundary