scholarly journals The 1-soliton in theSO(3) gauged Skyrme model with mass term

Nonlinearity ◽  
2002 ◽  
Vol 15 (2) ◽  
pp. 385-392 ◽  
Author(s):  
Y Brihaye ◽  
J Burzlaff ◽  
V Paturyan ◽  
D H Tchrakian
Keyword(s):  
Mass Term ◽  
Skyrme Model

scholarly journals Near-BPS baby Skyrmions

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Sven Bjarke Gudnason ◽  
Marco Barsanti ◽  
Stefano Bolognesi
Keyword(s):  
Binding Energy ◽  
Topological Charge ◽  
Harmonic Maps ◽  
Single Point ◽  
Pion Mass ◽  
Mass Term ◽  
Skyrme Model ◽  
Classical Solutions ◽  
Leading Order ◽  
Area Preserving

Abstract We consider the baby-Skyrme model in the regime close to the so-called restricted baby-Skyrme model, which is a BPS model with area-preserving diffeomorphism invariance. The perturbation takes the form of the standard kinetic Dirichlet term with a small coefficient ϵ. Classical solutions of this model, to leading order in ϵ, are called restricted harmonic maps. In the BPS limit (ϵ → 0) of the model with the potential being the standard pion-mass term, the solution with unit topological charge is a compacton. Using analytical and numerical arguments we obtain solutions to the problem for topological sectors greater than one. We develop a perturbative scheme in ϵ with which we can calculate the corrections to the BPS mass. The leading order ($$ \mathcal{O}\left({\upepsilon}^1\right) $$ O ϵ 1 ) corrections show that the baby Skyrmion with topological charge two is energetically preferred. The binding energy requires us to go to the third order in ϵ to capture the relevant terms in perturbation theory, however, the binding energy contributes to the total energy at order ϵ2. We find that the baby Skyrmions — in the near-BPS regime — are compactons of topological charge two, that touch each other on their periphery at a single point and with orientations in the attractive channel.

A stealth defect of spacetime

2018 ◽  
Vol 33 (22) ◽  
pp. 1850127 ◽  
Author(s):  
F. R. Klinkhamer ◽  
J. M. Queiruga
Keyword(s):  
Energy Density ◽  
Long Range ◽  
Mass Term ◽  
Matter Field ◽  
Skyrme Model ◽  
Gravitational Mass ◽  
Positive Energy ◽  
Type Solution ◽  
Matter Fields

We discuss a special type of Skyrmion spacetime-defect solution, which has a positive energy density of the matter fields but a vanishing asymptotic gravitational mass. With a mass term for the matter field added to the action (corresponding to massive “pions” in the Skyrme model), this particular soliton-type solution has no long-range fields and can appropriately be called a “stealth defect”.

scholarly journals Steady Euler flows and the Faddeev-Skyrme model with mass term

2015 ◽  
Vol 56 (2) ◽  
pp. 023102 ◽  
Author(s):  
Radu Slobodeanu
Keyword(s):  
Mass Term ◽  
Skyrme Model ◽  
Euler Flows

scholarly journals Finkelstein–Rubinstein constraints for the Skyrme model with pion masses

2006 ◽  
Vol 462 (2071) ◽  
pp. 2001-2016 ◽  
Author(s):  
Steffen Krusch
Keyword(s):  
Nuclear Physics ◽  
Pion Mass ◽  
Classical Field Theory ◽  
Mass Term ◽  
Baryon Number ◽  
Skyrme Model ◽  
Classical Field ◽  
Rational Maps ◽  
Rational Map ◽  
Atomic Nuclei

The Skyrme model is a classical field theory modelling the strong interaction between atomic nuclei. It has to be quantized in order to compare it to nuclear physics. When the Skyrme model is semi-classically quantized it is important to take the Finkelstein–Rubinstein constraints into account. Recently, a simple formula has been derived to calculate the constraints for Skyrmions which are well approximated by rational maps. However, if a pion mass term is included in the model, Skyrmions of sufficiently large baryon number are no longer well approximated by the rational map ansatz. This paper addresses the question how to calculate Finkelstein–Rubinstein constraints for Skyrme configurations which are only known numerically.

scholarly journals Near-BPS baby Skyrmions with Gaussian tails

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Sven Bjarke Gudnason ◽  
Marco Barsanti ◽  
Stefano Bolognesi
Keyword(s):  
Pion Mass ◽  
Mass Term ◽  
Analytic Form ◽  
Case Finding ◽  
Skyrme Model ◽  
Numerical Computations ◽  
Small Coefficient ◽  
Diffeomorphism Invariance ◽  
Area Preserving

Abstract We consider the baby Skyrme model in a physically motivated limit of reaching the restricted or BPS baby Skyrme model, which is a model that enjoys area-preserving diffeomorphism invariance. The perturbation consists of the kinetic Dirichlet term with a small coefficient ϵ as well as the standard pion mass term, with coefficient $$ \upepsilon {m}_1^2 $$ ϵ m 1 2 . The pions remain lighter than the soliton for any ϵ and therefore the model is physically acceptable, even in the ϵ → 0 limit. The version of the BPS baby Skyrme model we use has BPS solutions with Gaussian tails. We perform full numerical computations in the ϵ → 0 limit and even reach the strict ϵ = 0 case, finding new nontrivial BPS solutions, for which we do not yet know the analytic form.

scholarly journals An improved holographic nodal line semimetal

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Yan Liu ◽  
Xin-Meng Wu
Keyword(s):  
Mass Term ◽  
Nodal Line ◽  
Duality Relation ◽  
Strongly Coupled ◽  
Nodal Lines ◽  
Form Field ◽  
Improved Model ◽  
Fermionic Spectrum ◽  
Chern Simons ◽  
Tensor Operators

Abstract We study an improved holographic model for the strongly coupled nodal line semimetal which satisfies the duality relation between the rank two tensor operators $$ \overline{\psi}{\gamma}^{\mu v}\psi $$ ψ ¯ γ μv ψ and $$ \overline{\psi}{\gamma}^{\mu v}{\gamma}^5\psi $$ ψ ¯ γ μv γ 5 ψ . We introduce a Chern-Simons term and a mass term in the bulk for a complex two form field which is dual to the above tensor operators and the duality relation is automatically satisfied from holography. We find that there exists a quantum phase transition from a topological nodal line semimetal phase to a trivial phase. In the topological phase, there exist multiple nodal lines in the fermionic spectrum which are topologically nontrivial. The bulk geometries are different from the previous model without the duality constraint, while the resulting properties are qualitatively similar to those in that model. This improved model provides a more natural ground to analyze transports or other properties of strongly coupled nodal line semimetals.

Quantum-mechanical treatment of the Skyrme Lagrangean, and a new mass term

1987 ◽  
Vol 58 (7) ◽  
pp. 651-653 ◽  
Author(s):  
K. Fujii ◽  
K-I. Sato ◽  
N. Toyota ◽  
A. P. Kobushkin
Keyword(s):  
Mechanical Treatment ◽  
Mass Term ◽  
Quantum Mechanical ◽  
Quantum Mechanical Treatment

scholarly journals Bogomolny equations for the BPS Skyrme models with impurity

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Ł.T. Stępień
Keyword(s):  
Skyrme Model

Abstract We show that the BPS Skyrme model, as well as its (2+1) dimensional baby version (restricted), can be coupled with an impurity in the BPS preserving manner. The corresponding Bogomolny equations are derived.

scholarly journals Temperature-Induced Plasmon Excitations for the α–T3 Lattice in Perpendicular Magnetic Field

Nanomaterials ◽  
2021 ◽  
Vol 11 (7) ◽  
pp. 1720
Author(s):  
Antonios Balassis ◽  
Godfrey Gumbs ◽  
Oleksiy Roslyak
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Zeeman Splitting ◽  
Mass Term ◽  
Energy Dispersive Spectrum ◽  
Wave Functions ◽  
Transition Energies ◽  
Gap Opening ◽  
Quantizing Magnetic Field

We have investigated the α–T3 model in the presence of a mass term which opens a gap in the energy dispersive spectrum, as well as under a uniform perpendicular quantizing magnetic field. The gap opening mass term plays the role of Zeeman splitting at low magnetic fields for this pseudospin-1 system, and, as a consequence, we are able to compare physical properties of the the α–T3 model at low and high magnetic fields. Specifically, we explore the magnetoplasmon dispersion relation in these two extreme limits. Central to the calculation of these collective modes is the dielectric function which is determined by the polarizability of the system. This latter function is generated by transition energies between subband states, as well as the overlap of their wave functions.

scholarly journals TOPOLOGICAL INSULATOR AND THE DIRAC EQUATION

SPIN ◽  
2011 ◽  
Vol 01 (01) ◽  
pp. 33-44 ◽  
Author(s):  
SHUN-QING SHEN ◽  
WEN-YU SHAN ◽  
HAI-ZHOU LU
Keyword(s):  
Dirac Equation ◽  
Topological Insulator ◽  
Bound States ◽  
Topological Insulators ◽  
Mass Term ◽  
Point Of View ◽  
Quadratic Term ◽  
General Description ◽  
Dirac Equations ◽  
Topological Quantum

We present a general description of topological insulators from the point of view of Dirac equations. The Z2 index for the Dirac equation is always zero, and thus the Dirac equation is topologically trivial. After the quadratic term in momentum is introduced to correct the mass term m or the band gap of the Dirac equation, i.e., m → m − Bp2, the Z2 index is modified as 1 for mB > 0 and 0 for mB < 0. For a fixed B there exists a topological quantum phase transition from a topologically trivial system to a nontrivial system when the sign of mass m changes. A series of solutions near the boundary in the modified Dirac equation is obtained, which is characteristic of topological insulator. From the solutions of the bound states and the Z2 index we establish a relation between the Dirac equation and topological insulators.

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