Asymmetric kink scattering in a two-component scalar field theory model

Producción CientíficaIn this paper the kink scattering in a two-component scalar field theory model in (1+1)-Minkowskian space-time is addressed. The potential term U(fi_1; fi_2) is given by a polynomial of fourth degree in the first field component and of sixth degree in the second one. The novel characteristic of this model is that the kink variety describes two different types of extended particles. These particles are characterized by its topological charge but also by a new feature determined by a discrete charge L = 0,1,-1. For this reason, the kink scattering involves a very rich variety of processes, which comprises kink annihilation, reflection, charge exchange, transmutation, etc. It has been found that not only the final velocity of the scattered kinks, but also the final nature of the emerging lumps after the collision are very sensitive on the initial velocities. Asymmetric scattering processes arise when Type I and Type II particles are obliged to collide. In this case, ten different final scenarios are possible. Symmetric scattering events are also discussed.In this paper the kink scattering in a two-component scalar field theory model in (1+1)-Minkowskian space-time is addressed. The potential term U(ϕ1, ϕ2) is given by a polynomial of fourth degree in the first field component and of sixth degree in the second one. The novel characteristic of this model is that the kink variety describes two different types of extended particles. These particles are characterized by its topological charge but also by a new feature determined by a discrete charge . For this reason, the kink scattering involves a very rich variety of processes, which comprises kink annihilation, reflection, charge exchange, transmutation, etc. It has been found that not only the final velocity of the scattered kinks, but also the final nature of the emerging lumps after the collision are very sensitive on the initial velocities. Asymmetric scattering processes arise when Type I and Type II particles are obliged to collide. In this case, ten different final scenarios are possible. Symmetric scattering events are also discussed.Ministerio de Economía, Ciencia y Competitividad (grant MTM2014-57129-C2-1-P)Junta de Castilla y Leon (grant VA057U16

Kink dynamics in the MSTB model

Producción CientíficaIn this paper kink scattering processes are investigated in the Montonen–Sarker–Trullinger–Bishop (MSTB) model. The MSTB model is in fact a one-parametric family of relativistic scalar field theories living in a one-time one-space Minkowski space-time which encompasses two coupled scalar fields. Among the static solutions of the model two kinds of topological kinks are distinguished in a precise range of the family parameter. In that regime there exists one unstable kink exhibiting only one non-null component of the scalar field. Another type of topological kink solutions, stable in this case, includes two different kinks for which the two components of the scalar field are non-null. Both one-component and two-component topological kinks are accompanied by their antikink partners. The decay of the unstable kink to one of the stable solutions plus radiation is numerically computed. The pair of stable two-component kinks living respectively on upper and lower semi-ellipses in the field space belongs to the same topological sector in the configuration space and provides an ideal playground to address several scattering events involving one kink and either its own antikink or the antikink of the other stable kink. By means of numerical analysis we shall find and describe interesting physical phenomena. Bion (kink–antikink oscillations) formation, kink reflection, kink–antikink annihilation, kink transmutation and resonances are examples of these types of events. The appearance of these phenomena emerging in the kink–antikink scattering depends critically on the initial collision velocity and the chosen value of the coupling constant parametrizing the family of MSTB models.MINDECO grant MTM2014-57129-C2-1-P and Junta de Castilla y León grants VA057U16 and BU229P18

Quantum-induced interactions in the moduli space of degenerate BPS domain walls

In this paper quantum effects are investigated in a very special two-scalar field model having a moduli space of BPS topological defects. In a $(1+1)$-dimensional space-time the defects are classically degenerate in mass kinks, but in $(3+1)$ dimensions the kinks become BPS domain walls, all of them sharing the same surface tension at the classical level. The heat kernel/zeta function regularization method will be used to control the divergences induced by the quantum kink and domain wall fluctuations. A generalization of the Gilkey-DeWitt-Avramidi heat kernel expansion will be developed in order to accommodate the infrared divergences due to zero modes in the spectra of the second-order kink and domain wall fluctuation operators, which are respectively $N\times N$ matrix ordinary or partial differential operators. Use of these tools in the spectral zeta function associated with the Hessian operators paves the way to obtain general formulas for the one-loop kink mass and domain wall tension shifts in any $(1+1)$- or $(3+1)$-dimensional $N$-component scalar field theory model. Application of these formulae to the BPS kinks or domain walls of the $N=2$ model mentioned above reveals the breaking of the classical mass or surface tension degeneracy at the quantum level. Because the main parameter distinguishing each member in the BPS kink or domain wall moduli space is essentially the distance between the centers of two basic kinks or walls, the breaking of the degeneracy amounts to the surge in quantum-induced forces between the two constituent topological defects. The differences in surface tension induced by one-loop fluctuations of BPS walls give rise mainly to attractive forces between the constituent walls except if the two basic walls are very far apart. Repulsive forces between two close walls only arise if the coupling is approaches the critical value from below.Comment: 34 pages, 7 figures, to appear in JHE

On a family of (1+1)-dimensional scalar field theory models: kinks, stability, one-loop mass shifts

In this paper we construct a one-parametric family of (1+1)-dimensional one-component scalar field theory models supporting kinks. Inspired by the sine-Gordon and $\phi^4$ models, we look at all possible extensions such that the kink second-order fluctuation operators are Schr\"odinger differential operators with P\"oschl-Teller potential wells. In this situation, the associated spectral problem is solvable and therefore we shall succeed in analyzing the kink stability completely and in computing the one-loop quantum correction to the kink mass exactly. When the parameter is a natural number, the family becomes the hierarchy for which the potential wells are reflectionless, the two first levels of the hierarchy being the sine-Gordon and $\phi^4$ models.Comment: 23 pages, 4 figures, to be published in Annals of Physic

Higgs phase in a gauge U(1)\mathbf{U}(1) non-linear CP1\mathbf{CP}^1-model. Two species of BPS vortices and their zero modes

In this paper zero modes of fluctuation are dissected around the two species of BPS vortices existing in the critical Higgs phase, where the scalar and vector meson masses are equal, of a gauged $\mathbb{U}(1)$ nonlinear $\mathbb{CP}^1$-model. If $2\pi n$, $n\in \mathbb{Z}$, is the quantized magnetic flux of the two species of BPS vortex solutions, $2n$ linearly independent vortex zero modes for each species are found and described. The existence of two species of moduli spaces of dimension $2n$ of these stringy topological defects is thus locally shown.Comment: 17 pages, 28 figure

Migratory experiences in United Kingdom: An opportunity to rethink leadership in the exercise of citizenship and its educational implications

El incremento de la emigración desde el Estado español durante los últimos años, a partir del estallido de la crisis socioeconómica y política en el sur de Europa, ha orientado su flujo especialmente a Reino Unido como primer destino europeo. La auto-organización de las personas emigradas en redes informales de acogida, apoyo y protesta, ofrece la oportunidad de atender a lo que dicen y hacen estas personas como material para nutrir reflexiones, donde lo académico dialogue con lo militante, en torno a la articulación del liderazgo en el aprendizaje de la ciudadanía desde su ejercicio práctico inserto en la vida cotidiana, como forma de extraer observaciones que puedan convertirse en aportaciones significativas en el campo de los estudios sobre procesos educativos. Además, la presentación de esta experiencia trata de contribuir al repensar colectivo sobre el concepto de “ciudadanía”, enmarcándose en el trabajo que, desde el enfoque intercultural, se realiza en el Grupo INTERThe increase of emigration from the Spanish State during the last years, from the “outbreak” of the socio-economic and political crisis in the south of Europe, has oriented the special flow to the United Kingdom as the first European destination. The self-organization of the emigrated people in informal networks of reception, support and protest, offers the opportunity to attend attend to what those people say and do as material to nourish reflections, where the academic dialogue with the militant, around the articulation of the leadership in the learning of citizenship from its practical exercise, inserted in daily life, as a way of extracting itself, which becomes significant contributions in the field of studies on educational processes. In addition, the presentation of this experience tries to contribute to rethinking the collective on the concept of "citizenship", framed in the work that, from the intercultural approach, is carried out in the INTER Grou

Two Species of Vortices in a massive Gauged Non-linear Sigma Model

Non-linear sigma models with scalar fields taking values on $\mathbb{C}\mathbb{P}^n$ complex manifolds are addressed. In the simplest $n=1$ case, where the target manifold is the $\mathbb{S}^2$ sphere, we describe the scalar fields by means of stereographic maps. In this case when the $\mathbb{U}(1)$ 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 self-dual 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 $\mathbb{C}\mathbb{P}^2$ 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 $\mathbb{U}(1)\times\mathbb{S}\mathbb{U}(2)$ 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 $\mathbb{C}\mathbb{P}^N$ models.Comment: 39 pages, 23 figures (extended version), to be published in JHE

Dissecting zero modes and bound states on BPS vortices in Ginzburg-Landau superconductors

In this paper the zero modes of fluctuation of cylindrically symmetric self-dual vortices are analyzed and described in full detail. These BPS topological defects arise at the critical point between Type II and Type I superconductors, or, equivalently, when the masses of the Higgs particle and the vector boson in the Abelian Higgs model are equal. In addition, novel bound states of Higss and vector bosons trapped by the self-dual vortices at their core are found and investigated.Comment: 29 pages, 51 figure

Dilemas éticos en trabajo social : el modelo de la Ley Social = Ethical dilemmas in social work : social-law decision-making model

E l objetivo de este artículo es estudiar los modelos de resolución de dilemas éticos utilizados en la profesión de trabajo social con el fin de analizar la toma de decisiones éticas en la práctica profesional. En el artículo se revisan los modelos de resolución de dilemas éticos desde el punto de vista de su aplicación a la profesión en dos grupos: modelos genéricos de toma de decisiones y modelos jerarquizantes. Como resultado de la investigación se propone un nuevo modelo de toma de decisiones éticas para la práctica profesional del trabajo social denominado “modelo de la ley social”, basado en los principios comunes a las tradiciones kantianas y utilitaristas del trabajo social con especial énfasis en el principio de justicia, que es común a ambas._________________________________________________The aim of this paper is to study the ethical dilemmas resolution models used in the social work profession in order to analyze ethical decision making in professional practice. The present article reviews the ethical-dilemas resolution models from the point of view of their application to the profession in two groups: generic models of decision-making and hierarchical models. As a result of this research we propose a new ethical decision-making model for social-work practice called “social law model” based on common principles to the Kantian and utilitarian traditions of social work with special emphasis on the principle of justice, which is common to both