Related papers: Aspects of Purely Transmitting Defects in Integrab…
Integrable inhomogeneous versions of the models like NLS, Toda chain, Ablowitz-Ladik model etc., though well known at the classical level, have never been investigated for their possible quantum extensions. We propose a unifying scheme for…
These lectures review certain topological defects and aspects of their cosmology. Unconventional material includes brief descriptions of electroweak defects, the structure of domain walls in non-Abelian theories, and the spectrum of…
The theory of Lie systems has recently been applied to Quantum Mechanics and additionally some integrability conditions for Lie systems of differential equations have also recently been analysed from a geometric perspective. In this paper…
We study the consistency of having Lorentz invariance as a low energy approximation within the quantum field theory framework. A model with a scalar and a fermion field is used to show how a Lorentz invariance violating high momentum scale,…
We associate bicomplexes with several integrable models in such a way that conserved currents are obtained by a simple iterative construction. Gauge transformations and dressings are discussed in this framework and several examples are…
We investigate higher grading integrable generalizations of the affine Toda systems. The extra fields, associated to non zero grade generators, obey field equations of the Dirac type and are regarded as matter fields. The models possess…
In a previous paper, we showed that the problem of tunneling in quantum wires was integrable in the isotropic case $g_\sigma=2$. In the present work, we continue the exploration of the general phase diagram by looking for other integrable…
We analyze the preparation (launching) of a 1D-propagating multipartite quantum soliton, its scattering and disintegration by an external potential. The regimes of suppressed disintegration and atom-number-dependent transmission are…
This lecture presents a short review of the main features of diffractive processes and QCD inspired models. It includes the following topics: (1) Quantum mechanics of diffraction: general properties; (2) Color dipole description of…
We explore boundary scattering in the sine-Gordon model with a non-integrable family of Robin boundary conditions. The soliton content of the field after collision is analysed using a numerical implementation of the direct scattering…
These are a set of lecture notes on generalized global symmetries in quantum field theory. The focus is on invertible symmetries with a few comments regarding non-invertible symmetries. The main topics covered are the basics of higher-form…
We examine the question of the integrability of the recently defined $\mathbb{Z}_2\times \mathbb{Z}_2$-graded sine-Gordon model, which is a natural generalisation of the supersymmetric sine-Gordon equation. We do this via appropriate…
We present here a set of lecture notes on tomography. The Radon transform and some of its generalizations are considered and their inversion formulae are proved. We will also look from a group-theoretc point of view at the more general…
This is a write-up of lectures on integrable sigma-models, which covers the following topics: (1) Homogeneous spaces, (2) Classical integrability of sigma-models in two dimensions, (3) Topological terms, (4) Background-field method and…
We review applications of the sine-Gordon model, the O(3) non-linear sigma model, the U(1) Thirring model, and the O(N) Gross--Neveu model to quasi one-dimensional quantum magnets, Mott insulators, and carbon nanotubes. We focus upon the…
Deformations of quantum field theories which preserve Poincar\'e covariance and localization in wedges are a novel tool in the analysis and construction of model theories. Here a general scenario for such deformations is discussed, and an…
The coupling between localized magnetic moments and itinerant electrons presents a plethora of interesting physics. The low-energy physics of some quantum impurity systems can be described using conformal field theory (CFT). In this paper,…
A method is introduced for constructing lattice discretizations of large classes of integrable quantum field theories. The method proceeds in two steps: The quantum algebraic structure underlying the integrability of the model is determined…
This review paper explores the Riccati-type pseudo-potential formulation applied to the quasi-integrable sine-Gordon, KdV, and NLS models. The proposed framework provides a unified methodology for analyzing quasi-integrability properties…
We discuss integrable many-body systems in one dimension of Calogero-Moser-Sutherland type, both classical and quantum as well as nonrelativistic and relativistic. In particular, we consider fundamental properties such as integrability, the…