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.

scholarly journals Hamiltonian Formulation of Quantum Hall Skyrmions with Hopf Term

1997 ◽  
Vol 12 (09) ◽  
pp. 619-630 ◽  
Author(s):  
B. Chakraborty ◽  
T. R. Govindarajan
Keyword(s):  
Angular Momentum ◽  
Sigma Model ◽  
Quantum Hall ◽  
Hamiltonian Formulation ◽  
Nonlinear Sigma Model ◽  
Quantum Hall Systems ◽  
Hamiltonian Analysis

We study the nonrelativistic nonlinear sigma model with Hopf term in this letter. This is an important issue because of its relation to the currently interesting studies in skyrmions in quantum Hall systems. We perform the Hamiltonian analysis of this system in CP1 variables. When the coefficient of the Hopf term becomes zero we get the Landau–Lifshitz description of the ferromagnets. The addition of Hopf term dramatically alters the Hamiltonian analysis. The spin algebra is modified giving a new structure and interpretation to the system. We point out momentum and angular momentum generators and new features they bring into the system.

FRACTIONAL STATISTICS INDUCED BY GAUGE FIELDS

1991 ◽  
Vol 06 (05) ◽  
pp. 391-398 ◽  
Author(s):  
ASHOK CHATTERJEE ◽  
V.V. SREEDHAR
Keyword(s):  
Gauge Theory ◽  
Gauge Field ◽  
Path Integral ◽  
Simple Proof ◽  
Scalar Particle ◽  
Gauge Fields ◽  
Fractional Statistics ◽  
Chern Simons

An explicit extension of Polyakov’s analysis of a scalar particle coupled to an Abelian Chern-Simons gauge theory to the case of two particles and arbitrary values of the coupling is given. A simple proof of the emergence of fractional statistics induced by the gauge field follows within the path-integral framework.

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).

Nonlinear sigma-model with a composite gauge field

1988 ◽  
Vol 31 (3) ◽  
pp. 191-194
Author(s):  
B. B. Lokhvitskii
Keyword(s):  
Gauge Field ◽  
Sigma Model ◽  
Nonlinear Sigma Model

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 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.

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