2007/06/30 by Gabor Zsolt Toth, Gábor Zsolt Tóth, Toth, Gabor Zsolt
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Bound state #Boundary value problem #FOS: Physical sciences #Hamiltonian (control theory) #High Energy Physics - Theory (hep-th) #Ising model #Mathematical analysis #Mathematical physics #Mathematics #Operator (biology) #Physics #Physics of Superconductivity and Magnetism #Quantum Chromodynamics and Particle Interactions #Quantum field theory #Quantum mechanics #Theoretical physics #hep-th
paper · pdf · doi:10.48550/arxiv.0707.0015
PhD thesis, 195 pages, v2: minor correction in section 3.4.1
openalex publication_date 2007/06/30 · arxiv created 2007/11/21 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
This thesis contains three main parts, which are largely independent. In the first part we deal with the boundary bootstrap in supersymmetric factorized scattering theory. We give a description of supersymmetry in the case when the space is a half-line and present rules for the determination of the representations in which higher level boundary bound states transform, and for the determination of the supersymmetric one-particle reflection matrix factors for the higher level boundary bound states. These rules apply under the condition that the bulk particles transform in the kink or in the boson-fermion representation. Examples for the application of these rules to specific models are also given. In the second part we investigate the problem whether the TCSA spectrum can be approximated by the spectrum of the original Hamiltonian operator in which the coefficients of the terms are suitably changed. The investigation is done in the case of the critical Ising model on a strip with an external magnetic field on one of the boundaries. Another truncation method that preserves the solvability of the model is also considered. The results of perturbative and numerical calculations show that the above approximation is possible and that the qualitative behaviour of the truncated spectrum as a function of the coupling constant depends on the truncation method. In the third part we investigate the phase structure of the two- and three-frequency sine-Gordon models using the TCSA. In the case of the three-frequency model the tricritical point, several points of the critical line and a few points of the line of first order transition are found.