scholarly journals QUANTUM HALL SKYRMIONS IN THE FRAMEWORK OF O(4) NONLINEAR SIGMA MODEL

2004 ◽  
Vol 18 (02) ◽  
pp. 171-184
Author(s):  
B. BASU ◽  
S. DHAR ◽  
P. BANDYOPADHYAY
Keyword(s):  
Sigma Model ◽  
Quantum Hall ◽  
Nonlinear Sigma Model ◽  
New Framework ◽  
Spin And Statistics

A new framework for quantum Hall skyrmions in O(4) nonlinear sigma model is studied here. The size and energy of the skyrmions are determined incorporating the quartic stability term in the Lagrangian. Moreover, the introduction of a θ-term determines the spin and statistics of these 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.

SOLITON OPERATORS OF FRACTIONAL SPIN IN 2+1 DIMENSIONS

1991 ◽  
Vol 06 (08) ◽  
pp. 1369-1383 ◽  
Author(s):  
DIMITRA KARABALI
Keyword(s):  
Configuration Space ◽  
Sigma Model ◽  
Canonical Quantization ◽  
Nonlinear Sigma Model ◽  
Flat Connection ◽  
Fractional Spin ◽  
Spin And Statistics

Soliton operators of fractional spin and statistics are constructed using canonical quantization of the O(3) nonlinear sigma model with a topological Hopf action in 2+1 dimensions. The role of the Hopf term as the nontrivial holonomy of a flat connection in the configuration space is emphasized.

scholarly journals Massive gravity from double copy

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Arshia Momeni ◽  
Justinas Rumbutis ◽  
Andrew J. Tolley
Keyword(s):  
Sigma Model ◽  
Massive Gravity ◽  
Effective Field ◽  
Effective Theory ◽  
Nonlinear Sigma Model ◽  
Limit Theory ◽  
Four Dimensions ◽  
Yang Mills ◽  
Massive Spin ◽  
Double Copy

Abstract We consider the double copy of massive Yang-Mills theory in four dimensions, whose decoupling limit is a nonlinear sigma model. The latter may be regarded as the leading terms in the low energy effective theory of a heavy Higgs model, in which the Higgs has been integrated out. The obtained double copy effective field theory contains a massive spin-2, massive spin-1 and a massive spin-0 field, and we construct explicitly its interacting Lagrangian up to fourth order in fields. We find that up to this order, the spin-2 self interactions match those of the dRGT massive gravity theory, and that all the interactions are consistent with a Λ3 = (m2MPl)1/3 cutoff. We construct explicitly the Λ3 decoupling limit of this theory and show that it is equivalent to a bi-Galileon extension of the standard Λ3 massive gravity decoupling limit theory. Although it is known that the double copy of a nonlinear sigma model is a special Galileon, the decoupling limit of massive Yang-Mills theory is a more general Galileon theory. This demonstrates that the decoupling limit and double copy procedures do not commute and we clarify why this is the case in terms of the scaling of their kinematic factors.

scholarly journals An emergent universe supported by a nonlinear sigma model

2009 ◽  
Vol 26 (7) ◽  
pp. 075017 ◽  
Author(s):  
A Beesham ◽  
S V Chervon ◽  
S D Maharaj
Keyword(s):  
Sigma Model ◽  
Nonlinear Sigma Model ◽  
Emergent Universe

scholarly journals Isolated skyrmions in the CP2 nonlinear sigma model with a Dzyaloshinskii-Moriya type interaction

2021 ◽  
Vol 103 (6) ◽  
Author(s):  
Yutaka Akagi ◽  
Yuki Amari ◽  
Nobuyuki Sawado ◽  
Yakov Shnir
Keyword(s):  
Sigma Model ◽  
Nonlinear Sigma Model ◽  
Type Interaction
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