共查询到20条相似文献,搜索用时 31 毫秒
1.
《Physics letters. [Part B]》1988,207(1):39-43
By coupling an antisymmetric three-indexed gauge potential to a thick or solitonic membrane appearing in an SO(5) nonlinear σ model, we find that the physics describes the second Hopf map S7→S4. The resulting phase interaction between membranes provides an integral representation of the topological invariant. Using quarternionic fields, we can write the Hopf term in a local form. Remarkably, the three-indexed abelian gauge potential may be identified with the Chern-Simons form of an SU(2) gauge potential constructed out of the quanternion fields. 相似文献
2.
Peng-Ming Zhang Xi-Guo Lee Shao-Feng Wu 《International Journal of Theoretical Physics》2007,46(12):3234-3241
We investigate the solitons in the CP
N
model in terms of the decomposition of gauge potential. Based on the φ-mapping topological current theory, the charge and position of solitons is determined by the properties of the typical component.
Furthermore, the motion and the bifurcation of multi-soliton is discussed. And the knotted solitons in high dimension is explored
also. 相似文献
3.
We consider a (3+1)-dimensional local field theory defined on the sphere S
2. The model possesses exact soliton solutions with nontrivial Hopf topological charges and an infinite number of local conserved currents. We show that the Poisson bracket algebra of the corresponding charges is isomorphic to that of the area-preserving diffeomorphisms of the sphere S
2. We also show that the conserved currents under consideration are the Noether currents associated to the invariance of the Lagrangian under that infinite group of diffeomorphisms. We indicate possible generalizations of the model. 相似文献
4.
《Nuclear Physics B》1998,514(3):667-687
The Hopf term in the (2+ 1)-dimensional O(3) nonlinear sigma model, which is known to be responsible for fractional spin and statistics, is re-examined from the viewpoint of quantization ambiguity. It is confirmed that the Hopf term can be understood as a term induced quantum mechanically, in precisely the same manner as the θ-term in QCD. We present a detailed analysis of the topological aspect of the model based on the adjoint orbit parametrization of the spin vectors, which is not only very useful in handling topological (soliton and/or Hopf) numbers, but also plays a crucial role in defining the Hopf term for configurations of nonvanishing soliton numbers. The Hopf term is seen to arise explicitly as a quantum effect which emerges when quantizing an S1 degree of freedom hidden in the configuration space. 相似文献
5.
Possible topological solitons (skyrmions) of four-dimensional supersymmetric nonlinear σ-models are investigated. The requirements of supersymmetry limit our study to the CP1 model. A stable soliton seems possible, but in the absence of a demonstrated lower-bound for the mass, the stability of the soliton is unproved. The semi-classical spectrum of the CP1 skyrmion, as well as its supersymmetric extension, is studied. 相似文献
6.
Adil Belhaj 《Physics letters. [Part B]》2011,705(5):539-542
Using D-brane physics, we study fractional quantum Hall solitons (FQHS) in ABJM-like theory in terms of type IIA dual geometries. In particular, we discuss a class of Chern-Simons (CS) quivers describing FQHS systems at low energy. These CS quivers come from R-R gauge fields interacting with D6-branes wrapped on 4-cycles, which reside within a blown up CP3 projective space. Based on the CS quiver method and mimicking the construction of del Pezzo surfaces in terms of CP2, we first give a model which corresponds to a single layer model of FQHS system, then we propose a multi-layer system generalizing the doubled CS field theory, which is used in the study of topological defect in graphene. 相似文献
7.
In this paper we show how to quantize Hopf solitons using the Finkelstein-Rubinstein approach. Hopf solitons can be quantized
as fermions if their Hopf charge is odd. Symmetries of classical minimal energy configurations induce loops in configuration
space which give rise to constraints on the wave function. These constraints depend on whether the given loop is contractible.
Our method is to exploit the relationship between the configuration spaces of the Faddeev-Hopf and Skyrme models provided
by the Hopf fibration. We then use recent results in the Skyrme model to determine whether loops are contractible. We discuss
possible quantum ground states up to Hopf charge Q=7. 相似文献
8.
磁霍普夫子是一类新兴的三维磁拓扑孤子,具有精妙的三维自旋拓扑结构,可以展现丰富新奇的物理特性。随着最近磁霍普夫子研究的兴起,三维拓扑孤子相关的研究也进入了一个新的阶段。文章将简要介绍如何在固体磁性系统中实现稳定的磁霍普夫子,同时针对一个最简单的霍普夫子自旋结构,讨论其有趣的三维自旋动力学特性,为今后进一步研究霍普夫子和推进三维拓扑自旋电子学的发展抛砖引玉。 相似文献
9.
In a presumed dynamically broken, minimally coupled SU(2) model, a natural Higgs mass of order 1 TeV marks the onset of a strongly interacting Higgs sector probably rich in resonance structure and inaccessible to perturbation theory. In the spirit of the chiral dynamics approach to low-energy hadron physics, the heavy Higgs sector is here assumed to be well described up to one-loop effects by an SO(4) non-linear σ-model of the Skyrme type. Taken as an effective zeroth-order lagrangian, the latter is shown to admit two varieties of finite-energy, three-dimensional localized solitons which may exist in nature. They are given by the S3 → S3 Chern-Pontryagin maps and the S3 → S2 twisted toroid Hopf maps, respectively. Upper and lower bounds on the masses of the hedgehog and twisted ring with kink-number one are found to lie in the few TeV range. By a topological theorem of Finkelstein et al., both types of solitons provide classical analogues of superheavy fermion states. The connection between these solitons with other extended objects predicted by Nambu and Huang, and their possible experimental signatures are sketched. Finally, the extension of our results to the more realistic SU(2) × U(1) Weinberg-Salam model is discussed. 相似文献
10.
M. Faber 《Few-Body Systems》2001,30(3):149-186
We introduce a model designed to describe charged particles as stable topological solitons of a field with values on the
internal space S
3. These solitons behave like particles with relativistic properties like Lorentz contraction and velocity dependence of mass.
This mass is defined by the energy of the soliton. In this sense this model is a generalization of the Sine-Gordon model1(We do not chase the aim to give a four-dimensional generalization of Coleman’s isomorphism between the Sine-Gordon model
and the Thirring model which was shown in 2-dimensional space-time) from 1 + 1-dimensions to 3 + 1-dimensions, from S
1 to S
3. For large distances from the centre of solitons this model tends to a dual U(1)-theory with freely propagating electromagnetic waves. Already at the classical level it describes important effects, which
usually have to be explained by quantum field theory, like particle-antiparticle annihilation and the running of the coupling.
Received November 30, 1999; revised June 20, 2000; accepted for publication October 2, 2000 相似文献
11.
Peng-ming Zhang Xi-guo Lee Shao-feng Wu Yi-shi Duan 《International Journal of Theoretical Physics》2007,46(7):1753-1762
We study the wave dislocations with an induced gauge potential. The topological current characterized the wave dislocations
is constructed with the dual of Abelian gauge field. And the topological charges and locations of the wave dislocations are
determined by the φmapping topological current theory. Furthermore, it is shown that the knotted wave dislocations can be
described with a Hopf invariant in the wave field. At last we discussed the evolution of the knotted wave dislocations.
PACS 02.10.Kn, 02.40.-k, 11.15.-q 相似文献
12.
《Reports on Mathematical Physics》1999,43(1-2):271-281
We apply the coadjoint orbit method to construct relativistic nonlinear sigma models (NLSM) on the target space of coadjoint orbits coupled with the Chern-Simons (CS) gauge field and we study self-dual solitons. When the target space is given by a Hermitian symmetric space (HSS), we find that the system admits self-dual solitons whose energy is Bogomol'nyi bounded from below by a topological charge. The Bogomol'nyi potential on the Hermitian symmetric space is obtained in the case when the maximal torus subgroup is gauged, and the self-dual equation in the CP(N − 1) case is explored. We also discuss the self-dual solitons in the case of noncompact SU(1, 1) and present a detailed analysis for the rotationally symmetric solutions. 相似文献
13.
《Journal of Geometry and Physics》1997,23(1):65-75
We use the Neroslavsky-Vlassov (1981) method to find a star product h on a class of exact Poisson-Lie groups such that (C∞(G)[[h]], h, Δ) is a Hopf algebra. We show that we can find such a nontrivial star product on every Lie group. 相似文献
14.
By using a general symmetry theory related to invariant functions,strong symmetry operators and hereditary operators,we find a general integrable hopf heirarchy with infinitely many general symmetries and Lax pairs.For the first order Hopf equation,there exist infinitely many symmetries which can be expressed by means of an arbitrary function in arbitrary dimensions.The general solution of the first order Hopf equation is obtained via hodograph transformation.For the second order Hopf equation,the Hopf-diffusion equation,there are five sets of infinitely many symmetries.Especially,there exist a set of primary branch symmetry with which contains an arbitrary solution of the usual linear diffusion equation.Some special implicit exact group invariant solutions of the Hopf-diffusion equation are also given. 相似文献
15.
We construct a new 2-parameter family of static topological solitons in 5D minimal supergravity which are endowed with magnetic charge and mass. The solitons are asymptotically R4×S1, where the radius of the S1 has a lower bound Rs?Rmin. Setting up initial data on a Cauchy slice at a moment of time symmetry, we demonstrate that if Rs>Rmin these solitons correspond to a perturbatively stable “small” static bubble as well as an unstable “large” static bubble, whereas if Rs<Rmin there are no static bubbles. The energetics and thermodynamics of the magnetic black string are then discussed and it is shown that the locally stable bubble is the end point of a phase transition for an appropriate range of black string parameters. 相似文献
16.
In this paper, we study the generalized quantum double construction for paired Hopf algebras with particular attention to
the case when the generalized quantum double is a Hopf algebra with projection. Applying our theory to a coquasitriangular
Hopf algebra (H, σ), we see that H has an associated structure of braided Hopf algebra in the category of Yetter-Drinfeld modules over , where H
σ
is a subHopf algebra of H
0, the finite dual of H. Specializing to the quantum group H = SL
q
(N), we find that H
σ
is , so that the duality between these quantum groups is just the evaluation map. Furthermore, we obtain explicit formulas for
the braided Hopf algebra structure of SL
q
(N) in the category of left Yetter-Drinfeld modules over .
The second author held a postdoctoral fellowship at Mount Allison University from 2005 to 2007 and would like to thank Mount
Allison for their warm hospitality. Support for the first author’s research and partial support for the postdoctoral position
of the second author came from an NSERC Discovery Grant. The second author now holds research support from Grant 434/1.10.2007
of CNCSIS. 相似文献
17.
Using the spherical basis of the spin-ν operator, together with an appropriate normalized complex (2ν +1)-spinor on S 3 we obtain spin-ν representation of the U(1) Hopf fibration S 3 → S 2 as well as its associated fuzzy version. Also, to realize the first Hopf map via the spherical basis of the spin-1 operator with even winding numbers, we present an appropriate normalized complex three-spinor. We put the winding numbers in one-to-one correspondence with the monopole charges corresponding to different associated complex vector bundles. 相似文献
18.
Shogo Aoyama 《Nuclear Physics B》1980,168(2):354-364
The supersymmetry algebra is examined for the (2+1)-dimensional supersymmetric CPN?1 model, on the basis of the observation of Witten and Olive in (1+1) and (3+1) dimensions. We then demonstrate that also in this (2+1)-dimensional model the usual supersymmetry algebra is modified by the appearance of the topological numbers of the solitons, which are nothing but the instantons in (1+1) dimensions, as central charges. To obtain the model, we begin by constructing the supersymmetric model in (3+1) dimensions. Then it is reduced to (2+1) dimensions by means of the dimensional reduction technique. We observe that the (2+1)-dimensional supersymmetric CPN?1 model thus obtained admits an O(2) extended supersymmetry. 相似文献
19.
Three-dimensional stationary precession solitons with nonzero Hopf indices are found numerically by solving the Landau-Lifshitz equation. The structure and existence domain of the solitons are found. 相似文献
20.
We obtain the integrable relation for the one-dimensional
nonlinear Schrödinger equations which describes the dynamics
of a Bose-Einstein Condensates with time-dependent scattering
length in a harmonic potential. The exact one- and two-soliton
solutions are constructed analytically by using the Hirota method.
Then we further discuss the dynamics of the one soliton and the
interactions between two solitons in currently experimental
conditions. 相似文献