scholarly journals DIRAC QUANTIZATION OF A NONMINIMAL GAUGED O(3) SIGMA MODEL

2005 ◽  
Vol 20 (13) ◽  
pp. 1005-1012 ◽  
Author(s):  
K. C. MENDES ◽  
R. R. LANDIM ◽  
C. A. S. ALMEIDA
Keyword(s):  
Sigma Model ◽  
Nonlinear Sigma Model ◽  
Nonminimal Coupling ◽  
Dirac Quantization ◽  
Chern Simons

The (2+1)-dimensional gauged O(3) nonlinear sigma model with Chern–Simons term is canonically quantized. Furthermore, we study a nonminimal coupling in this model implemented by means of a Pauli-type term. It is shown that the set of constraints of the model is modified by the introduction of the Pauli coupling. Moreover, we found that the quantum commutator relations in the nominimal case is independent of the Chern–Simons coefficient, in contrast to the minimal one.

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.

scholarly journals BRST INVARIANT CP1 MODEL THROUGH IMPROVED DIRAC QUANTIZATION

2001 ◽  
Vol 16 (21) ◽  
pp. 1361-1376 ◽  
Author(s):  
SOON-TAE HONG ◽  
YOUNG-JAI PARK ◽  
KUNIHARU KUBODERA ◽  
FRED MYHRER
Keyword(s):  
Energy Spectrum ◽  
Path Integral ◽  
Sigma Model ◽  
Nonlinear Sigma Model ◽  
Rigid Rotator ◽  
Dirac Quantization ◽  
Collective Coordinate ◽  
Integral Procedure ◽  
Physical Fields ◽  
Invariant Gauge

The Batalin–Fradkin–Tyutin (BFT) scheme, which is an improved version of Dirac quantization, is applied to the CP1 model, and the compact form of a nontrivial first-class Hamiltonian is directly obtained by introducing the BFT physical fields. We also derive a BRST-invariant gauge fixed Lagrangian through the standard path-integral procedure. Furthermore, performing collective coordinate quantization we obtain energy spectrum of rigid rotator in the CP1 model. Exploiting the Hopf bundle, we also show that the CP1 model is exactly equivalent to the O(3) nonlinear sigma model at the canonical level.

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.

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.

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