arXiv subjects

Sabina Alazzawi

Publications and source records attributed to Sabina Alazzawi.

5 recordsLinked to original sources

arXiv2016

Inverse Scattering and Locality in Integrable Quantum Field Theories

We present a solution method for the inverse scattering problem for integrable two-dimensional relativistic quantum field theories, specified in terms of a given massive single particle spectrum and a factorizing S-matrix. An arbitrary number of massive particles transforming under an arbitrary compact global gauge group is allowed, thereby generalizing previous constructions of scalar theories. The two-particle S-matrix $S$ is assumed to be an analytic solution of the Yang-Baxter equation with standard properties, including unitarity, TCP invariance, and crossing symmetry. Using methods from operator algebras and complex analysis, we identify sufficient criteria on $S$ that imply the solution of the inverse scattering problem. These conditions are shown to be satisfied in particular by so-called diagonal S-matrices, but presumably also in other cases such as the $O(N)$-invariant nonlinear $σ$-models.

math-ph↗

arXiv2015

Compton scattering in the Buchholz-Roberts framework of relativistic QED

We consider a Haag-Kastler net in a positive energy representation, admitting massive Wigner particles and asymptotic fields of massless bosons. We show that states of the massive particles are always vacua of the massless asymptotic fields. Our argument is based on the Mean Ergodic Theorem in a certain extended Hilbert space. As an application of this result we construct the outgoing isometric wave operator for Compton scattering in QED in a class of representations recently proposed by Buchholz and Roberts. In the course of this analysis we use our new technique to further simplify scattering theory of massless bosons in the vacuum sector. A general discussion of the status of the infrared problem in the setting of Buchholz and Roberts is given.

math-ph↗

arXiv2015

Generalized Kraus Operators and Generators of Quantum Dynamical Semigroups

Quantum dynamical semigroups play an important role in the description of physical processes such as diffusion, radiative decay or other non-equilibrium events. Taking strongly continuous and trace preserving semigroups into consideration, we show that, under a special criterion, the generator of such a group admits a certain generalized standard form, thereby shedding new light on known approaches in this direction. Furthermore, we illustrate our analysis in concrete examples.

math-ph↗

arXiv2015

Deformations of Quantum Field Theories and the Construction of Interacting Models

The subject of this thesis is the rigorous construction of QFT models with nontrivial interaction. Two different approaches in the framework of AQFT are discussed. On the one hand, an inverse scattering problem is considered. A given factorizing S-matrix is thereby taken as the starting point of the construction. The particle spectrum taken into account involves an arbitrary number of massive particle species, transforming under a global gauge group. Starting from known wedge-local auxiliary fields, the transition to local theories is shown. To his end, we make use of the modular nuclearity condition and investigate certain maps from the wedge algebras, generated by the auxiliary fields, to the considered Hilbert space. Under a very plausible conjecture it is shown that these maps are nuclear, which implies the nontriviality of algebras associated with bounded regions in the sense that the Reeh-Schlieder property holds. A large class of integrable models with factorizing S-matrices in 1+1 dimensions can be constructed in this way. Among them are the O(N)-invariant nonlinear sigma-models. Deformation techniques, on the other hand, constitute a method of construction which may be applied in arbitrary spacetime dimensions. This approach starts from a known quantum field theoretic model which is subjected to a certain modification. Here, concretely, the model of a scalar massive Fermion was deformed. The emerging models are based on wedge-local fields, allowing for the computation of the two-particle S-matrix. The resulting scattering matrix depends on the deformation and differs from the one of the initial model. By restricting to 1+1 dimensions, the deformation method yields a large class of integrable models with factorizing S-matrices, including the Sinh-Gordon model.

math-ph↗

arXiv2012

Deformations of Fermionic Quantum Field Theories and Integrable Models

Considering the model of a scalar massive Fermion, it is shown that by means of deformation techniques it is possible to obtain all integrable quantum field theoretic models on two-dimensional Minkowski space which have factorizing S-matrices corresponding to two-particle scattering functions S_2 satisfying S_2(0) = -1. Among these models there is for example the Sinh-Gordon model. Our analysis provides a complement to recent developments regarding deformations of quantum field theories. The deformed model is investigated also in higher dimensions. In particular, locality and covariance properties are analyzed.

math-ph↗