2015/03/03 by Sabina Alazzawi, Alazzawi, Sabina
Mathematics · Physics and Astronomy · #81T05 #81T10 #81T40 #81U99 #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.1503.00897
openalex publication_date 2015/03/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The subject of this thesis is the rigorous construction of QFT models with\nnontrivial interaction. Two different approaches in the framework of AQFT are\ndiscussed. On the one hand, an inverse scattering problem is considered. A\ngiven factorizing S-matrix is thereby taken as the starting point of the\nconstruction. The particle spectrum taken into account involves an arbitrary\nnumber of massive particle species, transforming under a global gauge group.\nStarting from known wedge-local auxiliary fields, the transition to local\ntheories is shown. To his end, we make use of the modular nuclearity condition\nand investigate certain maps from the wedge algebras, generated by the\nauxiliary fields, to the considered Hilbert space. Under a very plausible\nconjecture it is shown that these maps are nuclear, which implies the\nnontriviality of algebras associated with bounded regions in the sense that the\nReeh-Schlieder property holds. A large class of integrable models with\nfactorizing S-matrices in 1+1 dimensions can be constructed in this way. Among\nthem are the O(N)-invariant nonlinear sigma-models. Deformation techniques, on\nthe other hand, constitute a method of construction which may be applied in\narbitrary spacetime dimensions. This approach starts from a known quantum field\ntheoretic model which is subjected to a certain modification. Here, concretely,\nthe model of a scalar massive Fermion was deformed. The emerging models are\nbased on wedge-local fields, allowing for the computation of the two-particle\nS-matrix. The resulting scattering matrix depends on the deformation and\ndiffers from the one of the initial model. By restricting to 1+1 dimensions,\nthe deformation method yields a large class of integrable models with\nfactorizing S-matrices, including the Sinh-Gordon model.\n