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Generating boundary conditions for integrable field theories using defects

Hills, Daniel (2016) Generating boundary conditions for integrable field theories using defects. PhD thesis, University of York.

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Abstract

In this thesis, we examine the construction and characteristics of generalised reflection matrices, within the a_1^(1), a_2^(1) and a_2^(2) integrable affine Toda field theories. In doing so, we generalise the existing finite-dimensional reflection matrices because our construction involves the dressing of an integrable boundary with a defect. Within this framework, an integrable defect's ability to store an unlimited amount of topological charge is exploited, therefore all generalised solutions are intrinsically infinite-dimensional and exhibit interesting features. Overall, further evidence of the rich interplay between integrable defects and boundaries is provided. It is hoped that the generalised solutions presented in this thesis are potential quantum analogues of more general classical integrable boundary conditions.

Item Type: Thesis (PhD)
Keywords: Integrability, Defects, Boundaries
Academic Units: The University of York > Mathematics (York)
Identification Number/EthosID: uk.bl.ethos.707138
Depositing User: Mr Daniel Hills
Date Deposited: 31 Mar 2017 16:08
Last Modified: 24 Jul 2018 15:21
URI: http://etheses.whiterose.ac.uk/id/eprint/16379

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