arXiv subjects
Publications and source records attributed to J. Mateos Guilarte.
We discuss the solitary wave solutions of a particular two-component scalar field model in two-dimensional Minkowski space. These solitary waves involve one, two or four lumps of energy. The adiabatic motion of these composite non-linear non-dispersive waves points to variations in shape.
The mass shift induced by one-loop quantum fluctuations on self-dual ANO vortices is computed using heat kernel/generalized zeta function regularization methods.
Superpotentials in ${\cal N}=2$ supersymmetric classical mechanics are no more than the Hamilton characteristic function of the Hamilton-Jacobi theory for the associated purely bosonic dynamical system. Modulo a global sign, there are several superpotentials ruling Hamilton-Jacobi separable supersymmetric systems, with a number of degrees of freedom greater than one. Here, we explore how supersymmetry and separability are entangled in the quantum version of this kind of system. We also show that the planar anisotropic harmonic oscillator and the two-Newtonian centers of force problem admit two non-equivalent supersymmetric extensions with different ground states and Yukawa couplings.
One-loop corrections to kink masses in a family of (1+1)-dimensional field theoretical models with two real scalar fields are computed. A generalized DHN formula applicable to potentials with and without reflection is obtained. It is shown how half-bound states arising in the spectrum of the second order fluctuation operator for one-component topological kinks and the vacuum play a central r$\hat{\rm o}$le in the computation of the kink Casimir energy. The issue of whether or not the kink degeneracy exhibited by this family of models at the classical level survives one-loop quantum fluctuations is addressed.
We discuss classical and quantum aspects of the dynamics of a family of domain walls arising in a generalized Wess-Zumino model. These domain walls can be embedded in ${\cal N}=1$ supergravity as exact solutions and are composed of two basic lumps.
Supersymmetric extensions of Hamilton-Jacobi separable Liouville mechanical systems with two degrees of freedom are defined. It is shown that supersymmetry can be implemented in this type of systems in two independent ways. The structure of the constants of motion is unveiled and the entanglement between integrability and supersymmetry is explored.
The generalization of the Maupertuis principle to second-order Variational Calculus is performed. The stability of the solutions of a natural dynamical system is thus analyzed via the extension of the Theorem of Jacobi. It is shown that the Morse Theory of the trajectories in the dynamical system is identical to the Morse Theory of geodesics in the Jacobi metric, even though the second-variation functionals around the action and the Jacobi length do not coincide. As a representative example, we apply this result to the study of the separatrix solutions of the Garnier System.
The low energy dynamics of degenerated BPS domain walls arising in a generalized Wess-Zumino model is described as geodesic motion in the space of these topological walls.
We use the generalized zeta function regularization method to compute the one-loop quantum correction to the masses of the TK1 and TK2 kinks in a deformation of the O(N) linear sigma model on the real line.
We identify the kinks of a deformed O(3) linear Sigma model as the solutions of a set of first-order systems of equations; the above model is a generalization of the MSTB model with a three-component scalar field. Taking into account certain kink energy sum rules we show that the variety of kinks has the structure of a moduli space that can be compactified in a fairly natural way. The generic kinks, however, are unstable and Morse Theory provides the framework for the analysis of kink stability.
A method for describing the quantum kink states in the semi-classical limit of several (1+1)-dimensional field theoretical models is developed. We use the generalized zeta function regularization method to compute the one-loop quantum correction to the masses of the kink in the sine-Gordon and cubic sinh-Gordon models and another two ${\rm P}(ϕ)_2$ systems with polynomial self-interactions.
In this paper we describe the moduli space of kinks in a class of systems of two coupled real scalar fields in (1+1) Minkowskian space-time. The main feature of the class is the spontaneous breaking of a discrete symmetry of (real) Ginzburg-Landau type that guarantees the existence of kink topological defects.
The Compton effect in a two-dimensional world is compared with the same process in ordinary three-dimensional space.
Planar Quantum Electrodynamics is developed when charged fermions are under the influence of a constant and homogeneous external magnetic field. We compute the cross-length for the scattering of optical/ultraviolet photons by Dirac-Landau electrons.
The bosonic second invariant of SuperLiouville models in supersymmetric classical mechanics is described.
It is shown how a integrable mechanical system provides all the localized static solutions of a deformation of the linear O(N)-sigma model in two space-time dimensions. The proof is based on the Hamilton-Jacobi separability of the mechanical analogue system that follows when time-independent field configurations are being considered. In particular, we describe the properties of the different kinds of kinks in such a way that a hierarchical structure of solitary wave manifolds emerges for distinct N.
The kinks of the (1+1)-dimensional Wess-Zumino model with polynomic superpotential are investigated and shown to be related to real algebraic curves.
Several issues concerning the self-dual solutions of the Chern-Simons-Higgs model are addressed. The topology of the configuration space of the model is analysed when the space manifold is either the plane or an infinite cylinder. We study the local structure of the moduli space of self-dual solitons in the second case by means of an index computation. It is shown how to manage the non-integer contribution to the heat-kernel supertrace due to the non-compactness of the base space. A physical picture of the local coordinates parametrizing the non-topological soliton moduli space arises .