scholarly journals Self-Dual Configurations in a Generalized Abelian Chern-Simons-Higgs Model with Explicit Breaking of the Lorentz Covariance

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
Rodolfo Casana ◽  
Lucas Sourrouille
Keyword(s):  
Magnetic Field ◽  
Soliton Solutions ◽  
Higgs Field ◽  
Higgs Model ◽  
Point Of View ◽  
The Self ◽  
Kinetic Term ◽  
Lorentz Covariance ◽  
Vortex Solutions ◽  
Chern Simons

We have studied the existence of self-dual solitonic solutions in a generalization of the Abelian Chern-Simons-Higgs model. Such a generalization introduces two different nonnegative functions,ω1(|ϕ|)andω(|ϕ|), which split the kinetic term of the Higgs field,|Dμϕ|2→ω1(|ϕ|)|D0ϕ|2-ω(|ϕ|)|Dkϕ|2, breaking explicitly the Lorentz covariance. We have shown that a clean implementation of the Bogomolnyi procedure only can be implemented whetherω(|ϕ|)∝β|ϕ|2β-2withβ≥1. The self-dual or Bogomolnyi equations produce an infinity number of soliton solutions by choosing conveniently the generalizing functionω1(|ϕ|)which must be able to provide a finite magnetic field. Also, we have shown that by properly choosing the generalizing functions it is possible to reproduce the Bogomolnyi equations of the Abelian Maxwell-Higgs and Chern-Simons-Higgs models. Finally, some new self-dual|ϕ|6-vortex solutions have been analyzed from both theoretical and numerical point of view.

Existence of topological multivortex solutions in the self-dual gauge theories

2000 ◽  
Vol 130 (6) ◽  
pp. 1293-1309 ◽  
Author(s):  
Jongmin Han
Keyword(s):  
Exponential Decay ◽  
Gauge Theories ◽  
Integral Formula ◽  
Higgs Model ◽  
The Self ◽  
Abelian Higgs Model ◽  
Decay Of Solutions ◽  
Vortex Solutions ◽  
Chern Simons

This paper is concerned with the existence of topological multivortex solutions in (2 + 1) self-dual gauge theories such as the classical abelian Higgs model or the Chern–Simons Higgs gauge theories. A general form of topological multivortex equations is presented with the inclusion of antivortices. Two kinds of solutions are considered; topological vortex solutions and topological vortex–antivortex solutions. We construct these solutions by super and subsolution methods, and derive the exponential decay of solutions at infinity and the quantized integral formula. As an application, we prove the existence of a topological multivortex solutions in a generalized Chern–Simons Higgs theory.

MAGNUS FORCES AND STATISTICS IN 2 + 1 DIMENSIONS

1990 ◽  
Vol 05 (11) ◽  
pp. 853-862 ◽  
Author(s):  
R. L. DAVIS
Keyword(s):  
Magnetic Field ◽  
Finite Size ◽  
Higgs Model ◽  
Magnus Force ◽  
Ginzburg Landau ◽  
Quasi Particle ◽  
Vortex Solutions ◽  
Path Dependent ◽  
Chern Simons ◽  
Particle Statistics

Spinning vortex solutions to the abelian Higgs model, not Nielsen-Olesen solutions, are appropriate to a Ginzburg-Landau description of superconductivity. The main physical distinction is that spinning vortices experience the Magnus force while Nielsen-Olesen vortices do not. In 2 + 1 dimensional superconductivity without a Chern-Simons interaction, the effect of the Magnus force is equivalent to that of a background fictitious magnetic field. Moreover, the phase obtained an interchanging two quasi-particles is always path-dependent. When a Chern-Simons term is added there is an additional localized Magnus flux at the vortex. For point-like vortices, the Chern-Simons interaction can be seen as defining their intrinsic statistics, but in realistic cases of vortices with finite size in strong Magnus fields the quasi-particle statistics are not well-defined.

scholarly journals Self-dual soliton solutions in a Chern–Simons-CP(1) model with a nonstandard kinetic term

2014 ◽  
Vol 29 (23) ◽  
pp. 1450124 ◽  
Author(s):  
Rodolfo Casana ◽  
Lucas Sourrouille
Keyword(s):  
Magnetic Flux ◽  
Topological Charge ◽  
Soliton Solutions ◽  
The Self ◽  
Kinetic Term ◽  
Chern Simons ◽  
Model Support

A generalization of the Chern–Simons-CP(1) model is considered by introducing a nonstandard kinetic term. For a particular case, of this nonstandard kinetic term, we show that the model support self-dual Bogomol'nyi equations. The Bogomol'nyi–Prasad–Sommerfield (BPS) energy has a bound proportional to the sum of the magnetic flux and the CP(1) topological charge. The self-dual equations are solved analytically and verified numerically.

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.

Non-Topological Multi-Vortex Solutions to the Self-Dual Chern-Simons-Higgs Equation

2002 ◽  
Vol 231 (2) ◽  
pp. 189-221 ◽  
Author(s):  
Hsungrow Chan ◽  
Chun-Chieh Fu ◽  
Chang-Shou Lin
Keyword(s):  
The Self ◽  
Vortex Solutions ◽  
Chern Simons

Coulomb Gauge Quantization and Renormalization of the Chern–Simons Theory Coupled to Fermions

1997 ◽  
Vol 12 (16) ◽  
pp. 2889-2901 ◽  
Author(s):  
M. Fleck ◽  
A. Foerster ◽  
H. O. Girotti ◽  
M. Gomes ◽  
J. R. S. Nascimento ◽  
...  
Keyword(s):  
Coulomb Gauge ◽  
The Self ◽  
Simons Theory ◽  
Fermion Propagator ◽  
Lorentz Covariance ◽  
Self Energy ◽  
The One ◽  
Chern Simons ◽  
Physical Quantities ◽  
Chern Simons Theory

We study the quantization and the one-loop renormalization of the model resulting from the coupling of charged fermions with a Chern–Simons field, in the Coulomb gauge. A proof of the Lorentz covariance of the physical quantities follows after establishing the Dirac–Schwinger algebra for the Poincaré densities and the transformation properties of the fields under the Poincaré group. The Coulomb gauge one-loop renormalization program is, afterwards, implemented. The noncovariant form of the one-loop fermion propagator, Chern–Simons field propagator and the vertex are explicitly obtained. Finally, the electron anomalous magnetic moment is calculated stressing that, due to the peculiarities of the Coulomb gauge, the contributions from the self-energy diagrams turn out to be essential.

VORTICES IN CURVED SPACE-TIME

1993 ◽  
Vol 08 (38) ◽  
pp. 3665-3672 ◽  
Author(s):  
J.D. EDELSTEIN ◽  
G. LOZANO ◽  
F.A. SCHAPOSNIK
Keyword(s):  
Scalar Curvature ◽  
Gauge Field ◽  
Space Time ◽  
Higgs Model ◽  
Curved Space ◽  
Abelian Higgs Model ◽  
Vortex Solutions ◽  
Chern Simons ◽  
Higgs Scalar

We study an Abelian Higgs model coupled to a background metric. We find Bogomol’nyi equations when the coupling is achieved through an Rɸ2 term (R being the scalar curvature and ɸ the Higgs scalar). Remarkably, these equations coincide with those arising in models where the gauge field dynamics is governed by a Chern-Simons term so that vortex solutions in our system can be related to self-dual Chern-Simons vortices.

scholarly journals Nontopological Condensates for the Self-Dual Chern-Simons-Higgs Model

2014 ◽  
Vol 68 (7) ◽  
pp. 1191-1283 ◽  
Author(s):  
Manuel del Pino ◽  
Pierpaolo Esposito ◽  
Pablo Figueroa ◽  
Monica Musso
Keyword(s):  
Higgs Model ◽  
The Self ◽  
Chern Simons
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