scholarly journals ON THE GAUGED NONCOMPACT SPIN SYSTEM

1998 ◽  
Vol 13 (32) ◽  
pp. 5503-5517
Author(s):  
SUNG-SOO KIM ◽  
PHILLIAL OH
Keyword(s):  
Spin System ◽  
Sigma Model ◽  
Soliton Solutions ◽  
Finite Energy ◽  
Nonlinear Sigma Model ◽  
Rotationally Symmetric ◽  
Background Charge ◽  
Chern Simons ◽  
Symmetric Soliton ◽  
Naive Model

We examine classical and quantum aspects of the planar noncompact spin system coupled with Chern–Simons gauge field in the presence of background charge. We first define our classical spin system as nonrelativistic nonlinear sigma model in which the order parameter spin takes value in the noncompact manifold ℳ= SU(1, 1)/U(1) . Although the naive model does not allow any finite energy self-dual solitons, it is shown that the gauged system admits static Bogomol'nyi solitons with finite energy whose rotationally symmetric soliton solutions are analyzed in detail. We also discuss the large spin limit in which the self-dual equation reduces to the well-known gauged nonlinear Schrödinger model or Abelian Higgs model, depending on the choice of the background charge term. Then, we perform quantization of the model. We find that the spin algebra satisfies anomalous commutation relations, and the system is a field theoretic realization of the anyons.

scholarly journals Self-Dual Chern–Simons Solitons in the Planar CP(1) Model

1997 ◽  
Vol 12 (40) ◽  
pp. 3169-3176 ◽  
Author(s):  
Yoonbai Kim ◽  
Phillial Oh ◽  
Chaiho Rim
Keyword(s):  
Gauge Field ◽  
Spin System ◽  
Soliton Solutions ◽  
The Self ◽  
Charge Densities ◽  
Rotationally Symmetric ◽  
Uniform Background ◽  
Background Charge ◽  
Chern Simons

We consider a nonrelativistic CP (1) system coupled minimally to an Abelian Chern–Simons gauge field and study the self-dual solitons which saturate the Bogomol'nyi bound. We find a rich structure of rotationally symmetric static soliton solutions for various uniform background charge densities. Possible application to spin system is mentioned.

scholarly journals THE EFFECTIVE LAGRANGIAN OF THREE DIMENSIONAL QUANTUM CHROMODYNAMICS

1992 ◽  
Vol 07 (32) ◽  
pp. 7989-8000 ◽  
Author(s):  
G. FERRETTI ◽  
S.G. RAJEEV ◽  
Z. YANG
Keyword(s):  
Quantum Chromodynamics ◽  
Sigma Model ◽  
Three Dimensional ◽  
Low Energy ◽  
Nonlinear Sigma Model ◽  
Flavor Symmetry ◽  
Energy Limit ◽  
Long Wavelength ◽  
Effective Lagrangian ◽  
Chern Simons

We consider the low energy limit of three dimensional quantum chromodynamics (QCD) with an even number of flavors. We show that parity is not spontaneously broken, but the global (flavor) symmetry is spontaneously broken. The low energy effective Lagrangian is a nonlinear sigma model on the Grassmannian. Some Chern-Simons terms are necessary in the Lagrangian to realize the discrete symmetries correctly. We consider also another parametrization of the low energy sector which leads to a three dimensional analogue of the Wess-Zumino-Witten-Novikov model. Since three dimensional QCD is believed to be a model for quantum antiferromagnetism, our effective Lagrangian can describe their long wavelength excitations (spin waves).

ADIABATIC ROTATION FOR THE SKYRMIONS

1993 ◽  
Vol 08 (37) ◽  
pp. 3569-3573
Author(s):  
ZHONG-SHUI MA
Keyword(s):  
Angular Momentum ◽  
Gauge Field ◽  
Sigma Model ◽  
Poynting Vector ◽  
Electromagnetic Properties ◽  
Nonlinear Sigma Model ◽  
Fractional Statistics ◽  
Rotation Procedure ◽  
Chern Simons ◽  
Explicit Derivation

We study the electromagnetic properties of the skyrmions of the O(3) nonlinear sigma model in (2+1) dimensions coupled with the Chern-Simons field by the adiabatic rotation procedure. It is shown that there is no Poynting vector for the skyrmion configuration and the Chern-Simons gauge field. In the process, an explicit derivation of the angular momentum is presented, which connects with the fractional statistics for the skyrmions.

TRANSVERSE LATTICE CONSTRUCTION OF 2+1 CHERN-SIMONS THEORY

1992 ◽  
Vol 07 (07) ◽  
pp. 601-610 ◽  
Author(s):  
PAUL A. GRIFFIN
Keyword(s):  
Lattice Model ◽  
Sigma Model ◽  
Simons Theory ◽  
Nonlinear Sigma Model ◽  
Expectation Values ◽  
Transverse Lattice ◽  
Lattice Construction ◽  
Chern Simons ◽  
Lattice Dimension ◽  
Chern Simons Theory

A transverse lattice model, with one lattice dimension and two continuum dimensions, is constructed by introducing Wess-Zumino terms into the gauged (1+1)-dimensional nonlinear sigma model action of the link fields. Its continuum limit is the pure Chern-Simons gauge theory in 2+1 dimensions. The lattice model is quantized, and some simple expectation values for Wilson loops on M2×S1 are evaluated. This construction provides an explicit connection between Chern-Simons theory and the gauged Wess-Zumino-Witten model.

scholarly journals Solitons of Some Nonlinear Sigma-Like Models

2020 ◽  
Author(s):  
V.E. Vekslerchik ◽  
Keyword(s):  
Sigma Model ◽  
Soliton Solutions ◽  
Nonlinear Sigma Model ◽  
Two Dimensional ◽  
Differential Identities ◽  
Yang Mills ◽  
Class Of Matrices

We present a set of differential identities for some class of matrices. These identities are used to derive the N-soliton solutions for the Pohlmeyer nonlinear sigma-model, two-dimensional self-dual Yang-Mills equations and some modification of the vector Calapso equation.

scholarly journals STRING-LIKE SOLUTIONS OF THE GAUGED NONLINEAR SIGMA MODEL

2004 ◽  
Vol 19 (21) ◽  
pp. 3595-3603
Author(s):  
HAMID REZA VANAIE ◽  
NEMATOLLAH RIAZI
Keyword(s):  
Sigma Model ◽  
Domain Walls ◽  
Unit Length ◽  
Energy Conditions ◽  
Nonlinear Sigma Model ◽  
Chern Simons ◽  
Least Energy

We show that the least energy conditions in the gauged nonlinear sigma model with Chern–Simons term lead to exact soliton-like solutions which look like domain walls. In fact, they are string-like solutions on the 2D plane. We will derive and discuss the corresponding solutions, and compute their energy and charge per unit length. The spin of the solutions is shown to vanish.

Sign in / Sign up

Export Citation Format

Share Document