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

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.

NUCLEI AS SUPERPOSITION OF TOPOLOGICAL SOLITONS

2008 ◽  
Vol 17 (01) ◽  
pp. 212-216
Author(s):  
A. ACUS ◽  
E. NORVAIŠAS ◽  
D. O RISKA
Keyword(s):  
Form Factor ◽  
Degrees Of Freedom ◽  
Canonical Quantization ◽  
Baryon Number ◽  
Skyrme Model ◽  
Light Nuclei ◽  
Electric Form Factor ◽  
Fundamental Representation ◽  
Rational Map ◽  
Topological Solitons

The rational map approximation provides an opportunity to describe light nuclei as classical solitons with baryon number B > 1 in the framework of the Skyrme model. The rational map ansatz yields a possibility of factorization of S3 baryon charge into S1 and S2 parts, the phenomenology of the model being strongly affected by the chosen factorization. Moreover, in the fundamental representation superposition of two different soliton factorizations can be used as solution ansatz. The canonical quantization procedure applied to collective degrees of freedom of the classical soliton leads to anomalous breaking of the chiral symmetry and exponential falloff of the energy density of the soliton at large distance, without explicit symmetry breaking terms included. The evolution of the shape of electric form factor as a function of two different factorization soliton mix ratio is investigated. Numerical results are presented.

scholarly journals SKYRMIONS, FULLERENES AND RATIONAL MAPS

2002 ◽  
Vol 14 (01) ◽  
pp. 29-85 ◽  
Author(s):  
RICHARD A. BATTYE ◽  
PAUL M. SUTCLIFFE
Keyword(s):  
Simulated Annealing Algorithm ◽  
Initial Conditions ◽  
Linear Time ◽  
Equations Of Motion ◽  
Baryon Number ◽  
Baryon Density ◽  
Rational Maps ◽  
Rational Map ◽  
Non Linear ◽  
Almost All

We apply two very different approaches to calculate Skyrmions with baryon number B ≤ 22. The first employs the rational map ansatz, where approximate charge B Skyrmions are constructed from a degree B rational map between Riemann spheres. We use a simulated annealing algorithm to search for the minimal energy rational map of a given degree B. The second involves the numerical solution of the full non-linear time dependent equations of motion, with initial conditions consisting of a number of well separated Skyrmion clusters. In general, we find a good agreement between the two approaches. For B ≥ 7 almost all the solutions are of fullerene type, that is, the baryon density isosurface consists of twelve pentagons and 2B - 14 hexagons arranged in a trivalent polyhedron. There are exceptional cases where this structure is modified, which we discuss in detail. We find that for a given value of B there are often many Skyrmions, with different symmetries, whose energies are very close to the minimal value, some of which we discuss. We present rational maps which are good approximations to these Skyrmions and accurately compute their energy by relaxation using the full non-linear dynamics.

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.

NUCLEAR DEFORMATIONS AS A SPONTANEOUS SYMMETRY BREAKING

1993 ◽  
Vol 02 (supp01) ◽  
pp. 51-69 ◽  
Author(s):  
WITOLD NAZAREWICZ
Keyword(s):  
Symmetry Breaking ◽  
Spontaneous Symmetry Breaking ◽  
Nuclear Physics ◽  
Particle Number ◽  
Building Blocks ◽  
Baryon Number ◽  
Strong Interactions ◽  
Fundamental Symmetries ◽  
Atomic Nuclei ◽  
Breaking Mechanism

Why can certain nuclei be described in terms of intrinsic shapes with non-spherical, triaxial, or reflection-asymmetric static moments? At first glance a violation of very fundamental symmetries such as rotational invariance, space inversion, or particle number symmetry is astonishing since strong interactions do actually conserve angular momentum, parity, and baryon number. The main building blocks of the spontaneous symmetry breaking mechanism in atomic nuclei are discussed and illuminated by examples taken from atomic and nuclear physics.

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