Homotopy and Solitons

Boya, Luis J.; Ena, José F. Cari; Mateos, Juan

doi:10.1002/prop.19780260303

Cited by 20 publications

(5 citation statements)

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“…There exists a firm opinion that classical field theory is differential geometry endowed with physical meaning, while quantum field theory one could expect to be related to random geometry. There are also some reviews and lecture notes, written on the so-called physical level of the mathematical rigor (Boya, Carinena and Mateos 1978;Hanson 1980, Olshanetskii 1982;, which might be recommended for rapid acquisition of basic concepts. The geometrical approach to the Skyrme model was pioneered in two remarkable a!…”

Section: Geometric Viewpoint On the Classical Field Theorymentioning

confidence: 99%

The Skyrme Model

Makhankov

Rybakov

Sanyuk

1993

Springer Series in Nuclear and Particle Physics

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Section: Geometric Viewpoint On the Classical Field Theorymentioning

confidence: 99%

The Skyrme Model

Makhankov

Rybakov

Sanyuk

1993

Springer Series in Nuclear and Particle Physics

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“…, which is a fibered space over CP N of dimension (N + 1) 2 − 1 and fiber U(N ), see [47], would be a good choice as target space because the possible BPS defects would have a topology related to the finite group Z N +1 with very interesting properties. In particular, the topology is due to the discrete subgroup Z N +1 a situation of the type discussed in [18] where twisted boundary conditions in the O(N ) sigma model break the discrete symmetry and give rise to fractional vortices,…”

Section: Jhep02(2015)139mentioning

confidence: 99%

Two species of vortices in massive gauged non-linear sigma models

Izquierdo

Fuertes

Guilarte

2015

J. High Energ. Phys.

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Non-linear sigma models with scalar fields taking values on CP n complex manifolds are addressed. In the simplest n = 1 case, where the target manifold is the S 2 sphere, we describe the scalar fields by means of stereographic maps. In this case when the U(1) symmetry is gauged and Maxwell and mass terms are allowed, the model accommodates stable self-dual vortices of two kinds with different energies per unit length and where the Higgs field winds at the cores around the two opposite poles of the sphere. Allowing for dielectric functions in the magnetic field, similar and richer self-dual vortices of different species in the south and north charts can be found by slightly modifying the potential. Two different situations are envisaged: either the vacuum orbit lies on a parallel in the sphere, or one pole and the same parallel form the vacuum orbit. Besides the selfdual vortices of two species, there exist BPS domain walls in the second case. Replacing the Maxwell contribution of the gauge field to the action by the second Chern-Simons secondary class, only possible in (2 + 1)-dimensional Minkowski space-time, new BPS topological defects of two species appear. Namely, both BPS vortices and domain ribbons in the south and the north charts exist because the vacuum orbit consits of the two poles and one parallel. Formulation of the gauged CP 2 model in a reference chart shows a self-dual structure such that BPS semi-local vortices exist. The transition functions to the second or third charts break the U(1) × SU(2) semi-local symmetry, but there is still room for standard self-dual vortices of the second species. The same structures encompassing N complex scalar fields are easily generalized to gauged CP N models.

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“…9) since P ElYl t For these solutions a topological charge can be introduced (The use of topological methods in the analysis of soliton solutions is described in more detail e.g. in [44])…”

Section: The Simplest Modelmentioning

confidence: 99%