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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…

We study properties of non-topological solitons in two-dimensional conformal field theory. The spectrum of linear perturbations on these solutions is found to be trivial, containing only symmetry-related zero modes. The interpretation of…

The classical soliton solution, quantized by means of suitable translational and rotational collective coordinates, is embedded into the one-particle irreductible representation of the Poincare group corresponding to a definite spin. It is…

We construct the soliton solutions in the symmetric space sine-Gordon theories. The latter are a series of integrable field theories in 1+1-dimensions which are associated to a symmetric space F/G, and are related via the Pohlmeyer…

The study of noncommutative solitons is greatly facilitated if the field equations are integrable, i.e. result from a linear system. For the example of a modified but integrable U(n) sigma model in 2+1 dimensions we employ the dressing…

We investigate the equation where the commutation relation in 2-dimensional zero-curvature equation composed of the algebra-valued potentials is replaced by the Moyal bracket and the algebra-valued potentials are replaced by the…

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…

In several self-coupled quantum field theories when treated in semi-classical limit one obtains solitonic solutions determined by topology of the boundary conditions. Such solutions, e.g. magnetic monopole in unified theories…

Zero modes of modular Hamiltonian of one interval are found in momentum space for two dimensional massless free scalar theory. Finite correlators are extracted from separate region connected correlation functions with the insertion of zero…

It has been observed that certain classical chains admit topologically protected zero-energy modes that are localized on the boundaries. The static features of such localized modes are captured by linearized equations of motion, but the…

The translation invariant model in quantum field theory is considered by functional integrations. Ultraviolet renormalization of the translation invariant Nelson model with a fixed total momentum is proven by functional integrations. As a…

Some soliton equation in 2+1 dimensions and their 1+1 and/or dimensional integrable reductions are considered.

We study rotationally symmetric translators for fully nonlinear extrinsic geometric flows driven by a curvature function, and we establish the fine asymptotics of bowl-type evolutions and, when admissible, the construction and…

Soliton solutions with cylindrical symmetry are investigated within the nonlinear $\sigma $-model disregarding the Skyrme-stabilization term. The solitons are stabilized by quantization of collective breathing mode and collapse in the…

A gauged (2+1)-dimensional version of the Skyrme model is investigated. The gauge group is $U(1)$ and the dynamics of the associated gauge potential is governed by a Maxwell term. In this model there are topologically stable soliton…

We calculate in this article the transport coefficients which characterize the dynamics of solitons in quantum field theory using the methods of dissipative quantum systems. We show how the damping and diffusion coefficients of soliton-like…

Various soliton-obstruction systems have been studied from analytical perspective. We have used collective coordinate to approach the dynamics of solitons as they meet a potential obstruction in a form of square barriers and holes for three…

For massive and conformal quantum field theories in 1+1 dimensions with a global gauge group we consider soliton automorphisms, viz. automorphisms of the quasilocal algebra which act like two different global symmetry transformations on the…

We obtain analytical expressions for an effective potential of interaction between two- and three-dimensional (2D and 3D) solitons (including the case of 2D vortex solitons) belonging to two different modes which are incoherently coupled by…

We construct an approximation to field theories on the noncommutative torus based on soliton projections and partial isometries which together form a matrix algebra of functions on the sum of two circles. The matrix quantum mechanics is…