Dynamics of solutions of the CP (N-1) models in (2+1) dimensions

The classical dynamics of slowly moving CP1 skyrmions in (2+1) dimensions is known to be described by the geodesic motion on a Kähler manifold of “quark” and “antiquark” constituents. This statement is reviewed here, and the problems of extending this result to skyrmions in other CP(N-1) models are discussed.     

Canonical structure of the CP sigma model in 1 + 2 dimensions

The CP^N model with a θ-term in 1 + 2 dimensions is quantized canonically. By employing a suitable parametrization we demonstrate that solitons carry θ-dependent fractional spins.     

Vector solitons in (2 + 1) dimensions

We address the problem of the existence and stability of vector spatial solitons formed by two incoherently interacting optical beams in bulk Kerr and saturable media. We identify families of (2+1)-dimensional two-mode self-trapped beams, with and without a topological charge, and describe their properties analytically and numerically.     

Spin transmutation in (2 + 1) dimensions

We study a relativistic anyon model with a spin-j matter field minimally coupled to an abelian Chem-Simons gauge field with a statistical parameter α. A spin and statistics transmutation is shown in terms of the continuum random walk method. An integer or odd-half-integer part of α can be reabsorbed by change of j. We discuss the equivalence of a large class of Chern-Simons matter models for given j and α.     

Traversible wormholes in (2 + 1) dimensions

We investigate traversible wormhole solutions to the Einstein field equations in (2 + 1) dimensions. The constraints on the field equations to obtain a wormhole solution are presented and further constraints for traversibility of the wormhole are also given. We show that there is no analog of the (3 + 1)-dimensional Schwarzschild wormhole in (2 + 1) dimensions. For general wormholes, the radial tension and lateral pressure at the throat of the wormhole must be zero, and the energy density must be negative. Two specific wormhole solutions are presented. We perform a stability analysis on the solutions.     

Model with solitons in (2+1) dimensions

We consider various models in (2+1) dimensions which possess soliton-like solutions. We discuss the additional terms that must be added to the conventionalS ² model in order that its solutions are stable and so can be treated as solitons. The role of various terms is analysed and some properties of the solitonic solutions are discussed.     

An eighth-order KdV-type equation in (1+1) and (2+1) dimensions: multiple soliton solutions

In this work we study an eighth-order KdV-type equations in (1+1) and (2+1) dimensions. The new equations are derived from the KdV6 hierarchy. We show that these equations give multiple soliton solutions the same as the multiple soliton solutions of the KdV6 hierarchy except for the dispersion relations.     

SU(2) Yang-Mills theory in (1 + 1) dimensions: A finite-lattice approach

Finite-lattice methods are used to calculate the masses of the lowest-lying baryon and meson states in the two-dimensional SU(2) Yang-Mills theory. No sign of a phase transition is seen at non-zero quark mass m. Both the meson and baryon mass vanish at m = 0: this is presumably a “chiral protection” mechanism.     

Combed hedgehog kink metric in (2+1) dimensions

A solution is presented for a rotating perfect fluid in (2+1)-dimensional spacetime. A complete metrical kink is seen to be present, provided that the boundary conditions are correctly formulated.     

Quasi-periodic and non-periodic waves in (2+1) dimensions

For a higher-dimensional integrable nonlinear dynamical system, there are abundant coherent soliton excitations. By means of the extended mapping approach, new exact quasi-periodic and non-periodic solutions for the (2+1)-dimensional nonlinear systems are displayed both analytically and graphically.     

Topology of quantum gauge fields and duality (I): Yang-Mills-Higgs system in 2 + 1 dimensions

The basic role of the representation of the gauge group in characterizing the topological excitations of the vacuum is pointed out. For SU(N) gauge fields on a lattice, the topological excitations are monopoles in the adjoint representation of the dual group ¹SU(N). This leads to a dual representation of the Yang-Mills-Higgs system in 2 + 1 dimensions. For SU(3) the deal theory in a scalar theory with discrete Weyl symmetry S₃. In the presence of adjoint Higgs fields the Weyl symmetry is broken in the Higgs phase but restored by pseudo-particles in the confinement phase.     

Skyrmions in (3+1) dimensions

We derive an analytical approximation to the skyrmion profile function. We check the quality of this approximation by using it to study various properties of the two skyrmion interactions. We find a good agreement with the numerical results of Verbaarschot et al. and Jackson et al.     

Bosonization in (1 + 1) dimensions: An elementary analysis

The expression of a free, massless, Fermi field in terms of scalar field components in a Lorentz basis is obtained. The infrared “disease” of the scalar field is seen to play a positive role in enforcing the fermionic selection rules. Particular attention is paid to the Poincaré transformation properties, both of the Fermi construct and of the Bose constituents. The way that two charge operators are contained in the scalar theory, and the necessary enlargement of the (indefinite metric) space on which the scalar field acts, are discussed in detail.     

Effective potential for scalar QED in (2+1) dimensions

We calculate the renormalized one loop approximation to the effective potential for scalar electrodynamics in (2+1) dimensions. We study its gauge dependence and show that it satisfies the renormalization group equation since it is independent on any renormalization scale. This relies on the fact that we do not need to improve the effective potential in (2+1) dimensions.     

Lax tensors and separable coordinates in (2+1) dimensions

We study the Lax tensors of the separable coordinates in (2+1) dimensions. The Lax tensors of the dual manifolds are investigated. Presented at the 9th Colloquium “Quantum Groups and Integrable Systems”, Prague, 22–24 June 2000.     

Ferromagnetic and antiferromagnetic properties of the blume-capel model in (1+1) and (2+1) dimensions

A renormalization group realization, allowing the simultaneous and analytic study of both the ferromagnetic and antiferromagnetic phases of the Blume-Capel model, is applied in (1+1)_and (2+1) dimensions. The model is also analyzed by using a variational technique. Critical and tricritical parameters are determined and the phase diagram is exhibited.Partially supported by CONICET, CIC Pcia. de Buenos Aires and SUBCYT, Argentina