Related papers: Aspects of Purely Transmitting Defects in Integrab…
Massive integrable field theories in $1+1$ dimensions are defined at the Lagrangian level, whose classical equations of motion are related to the ``non-abelian'' Toda field equations. They can be thought of as generalizations of the…
Defects are a useful tool in the study of quantum field theories. This is illustrated in the example of two-dimensional conformal field theories. We describe how defect lines and their junction points appear in the description of symmetries…
We present an inverse scattering approach to defects in classical integrable field theories. Integrability is proved systematically by constructing the generating function of the infinite set of modified integrals of motion. The…
Transmission matrices for two types of integrable defect are calculated explicitly, first by solving directly the nonlinear transmission Yang-Baxter equations, and second by solving a linear intertwining relation between a finite…
The structure of integrable field theories in the presence of jump defects is discussed in terms of boundary functions under the Lagrangian formalism. Explicit examples of bosonic and fermionic theories are considered. In particular, the…
Following our attempts to define quasi-integrability in which we related this concept to a particular symmetry of the two-soliton function we check this condition in three classes of modified Sine-Gordon models in (1+1) dimensions. We find…
A set of integral relations for rotational and translational zero modes in the vicinity of the classical soliton solution are derived from the particle-like properties of the latter. The validity of these all relations is considered for a…
In this paper, we first use semi-classical methods to study quantum field theoretical aspects of the integrable noncommutative sine-Gordon model proposed in [hep-th/0406065]. In particular, we examine the fluctuations at quadratic order…
Abstarct: Boundary effects caused by the boundary interactions in various integrable field theories on a half line are discussed at the classical as well as the quantum level. Only the so-called ``integrable" boundary interactions are…
The modern way to understand symmetries of a quantum field theory is via its topological defects in various dimensions. In this contribution to the proceedings we focus on line defects in 2d QFT and we point out that topological defects…
Profiles of static solitons in one-dimensional scalar field theory satisfy the same equations as trajectories of a fictitious particle in multidimensional mechanics. We argue that the structure and properties of the solitons are essentially…
We investigate several models described by real scalar fields, searching for topological defects. Some models are described by a single field, and support one or two topological sectors, and others are two-field models, which support…
Some aspects of the connection between differential geometry and multidimensional soliton equations are discussed.
In classical Lorentz-invariant field theories, localized soliton solutions necessarily break translation symmetry. In the corresponding quantum field theories, the position is quantized and, if the theory is not compactified, they have…
Sine-Gordon model with variable mass (VMSG) appears in many physical systems, ranging from the current through nonuniform Josephson junction to DNA-promoter dynamics. Such models are usually nonintegrable with solutions found numerically or…
Using the sine-Gordon model as the prime example an alternative approach to integrable boundary conditions for a theory restricted to a half-line is proposed. The main idea is to explore the consequences of taking into account the…
An integrable model possessing inhomogeneous ground states is proposed as an effective model of non-uniform quantum condensates such as supersolids and Fulde--Ferrell--Larkin--Ovchinnikov superfluids. The model is a higher-order analog of…
We describe a general way of constructing integrable defect theories as perturbations of conformal field theory by local defect operators. The method relies on folding the system onto a boundary field theory of twice the central charge. The…
The inverse scattering theory for the sine-Gordon equation discretized in space and both in space and time is considered.
Some soliton equation in 2+1 dimensions and their 1+1 and/or dimensional integrable reductions are considered.