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J. Mateos Guilarte

Publications and source records attributed to J. Mateos Guilarte.

At least 55 records · Page 3Linked to original sources
arXiv2009

BPS and non-BPS kinks in a massive non-linear S^2-sigma model

The stability of the kinks of the non-linear ${\mathbb S}^2$-sigma model discovered in Phys. Rev. Lett. 101(2008)131602 is discussed from several points of view. After a direct estimation of the spectra of the second-order fluctuation operators around topological kinks, first-order field equations are proposed to distinguish between BPS and non-BPS kinks. The one-loop mass shifts caused by quantum fluctuations around the topological kinks are computed using the Cahill-Comtet-Glauber formula proposed in Phys. Lett. 64B(1976)283. The (lack of) stability of the non-topological kinks is unveiled by application of the Morse index theorem. These kinks are identified as non-BPS states and the interplay between instability and supersymmetry is explored.

hep-th↗
arXiv2008

Construction of topological defect networks with complex scalar fields

This work deals with the construction of networks of topological defects in models described by a single complex scalar field. We take advantage of the deformation procedure recently used to describe kinklike defects in order to build networks of topological defects, which appear from complex field models with potentials that engender a finite number of isolated minima, both in the case where the minima present discrete symmetry, and in the non symmetric case. We show that the presence of symmetry guide us to the construction of regular networks, while the non symmetric case gives rise to irregular networks which spread throughout the complex field space. We also discuss bifurcation, a phenomenon that appear in the non symmetric case, but is washed out by the deformation procedure used in the present work.

hep-th↗
arXiv2008

Kinks in a non-linear massive sigma model

We describe the kink solitary waves of a massive non-linear sigma model with an ${\mathbb S}^2$ sphere as the target manifold. Our solutions form a moduli space of non-relativistic solitary waves in the long wavelength limit of ferromagnetic linear spin chains.

hep-th↗
arXiv2008

Constructing networks of defects with scalar fields

We propose a new way to build networks of defects. The idea takes advantage of the deformation procedure recently employed to describe defect structures, which we use to construct networks, spread from small rudimentary networks that appear in simple models of scalar fields.

hep-th↗
arXiv2008

One-loop fluctuations of semi-local self-dual vortices

Mass shifts induced by one-loop fluctuations of semi-local self-dual vortices are computed. The procedure is based on canonical quantization and heat kernel/ zeta function regularization methods. The issue of the survival of the classical degeneracy in the semi-classical regime is explored.

hep-th↗
arXiv2007

Two-Dimensional Supersymmetric Quantum Mechanics: Two Fixed Centers of Force

The problem of building supersymmetry in the quantum mechanics of two Coulombian centers of force is analyzed. It is shown that there are essentially two ways of proceeding. The spectral problems of the SUSY (scalar) Hamiltonians are quite similar and become tantamount to solving entangled families of Razavy and Whittaker-Hill equations in the first approach. When the two centers have the same strength, the Whittaker-Hill equations reduce to Mathieu equations. In the second approach, the spectral problems are much more difficult to solve but one can still find the zero-energy ground states.

math-ph↗
arXiv2007

One loop corrections to the mass of self-dual semi-local planar topological solitons

A formula is derived that allows the computation of one-loop mass shifts for self-dual semilocal topological solitons. These extended objects, which in three spatial dimensions are called semi-local strings, arise in a generalized Abelian Higgs model with a doublet of complex Higgs fields. Having a mixture of global, SU(2), and local (gauge), U(1), symmetries, this weird system may seem bizarre, but it is in fact the bosonic sector of electro-weak theory when the weak mixing angle is of 90 degrees. The procedure for computing the semi-classical mass shifts is based on canonical quantization and heat kernel/zeta function regularization methods.

hep-th↗
arXiv2007

Lectures on the mass of topological solitons

In this series of lectures a method is developed to compute one-loop shifts to classical masses of kinks, multi-component kinks, and self-dual vortices. Canonical quantization is used to show that the mass shift induced by one-loop quantum fluctuations is the trace of the square root of the differential operator governing these fluctuations. Standard mathematical techniques are used to deal with some powers of pseudo-differential operators. Ultraviolet divergences are tamed by using generalized zeta function regularization methods and, then performing zero-point energy and mass renormalizations.

hep-th↗
arXiv2007

A Class of Partially Solvable Two-Dimensional Quantum Models with Periodic Potentials

The supersymmetrical approach is used to analyse a class of two-dimensional quantum systems with periodic potentials. In particular, the method of SUSY-separation of variables allowed us to find a part of the energy spectra and the corresponding wave functions (partial solvability) for several models. These models are not amenable to conventional separation of variables, and they can be considered as two-dimensional generalizations of Lame, associated Lame, and trigonometric Razavy potentials. All these models have the symmetry operators of fourth order in momenta, and one of them (the Lame potential) obeys the property of self-isospectrality.

hep-th↗
arXiv2007

Orbit-based deformation procedure for two-field models

We present a method for generating new deformed solutions starting from systems of two real scalar fields for which defect solutions and orbits are known. The procedure generalizes the approach introduced in a previous work [Phys. Rev. D 66, 101701(R) (2002)], in which it is shown how to construct new models altogether with its defect solutions, in terms of the original model and solutions. As an illustration, we work out an explicit example in detail.

hep-th↗
arXiv2006

One-dimensional solitary waves in singular deformations of SO(2) invariant two-component scalar field theory models

In this paper we study the structure of the manifold of solitary waves in some deformations of SO(2) symmetric two-component scalar field theoretical models in two-dimensional Minkowski space. The deformation is chosen in order to make the analogous mechanical system Hamilton-Jacobi separable in polar coordinates and displays a singularity at the origin of the internal plane. The existence of the singularity confers interesting and intriguing properties to the solitary waves or kink solutions.

nlin.PS↗
arXiv2006

Deformed defects for scalar fields with polynomial interactions

In this paper we use the deformation procedure introduced in former work on deformed defects to investigate several new models for real scalar field. We introduce an interesting deformation function, from which we obtain two distinct families of models, labeled by the parameters that identify the deformation function. We investigate these models, which identify a broad class of polynomial interactions. We find exact solutions describing global defects, and we study the corresponding stability very carefully.

hep-th↗
arXiv2006

Two-Dimensional Supersymmetry: From SUSY Quantum Mechanics to Integrable Classical Models

Two known 2-dim SUSY quantum mechanical constructions - the direct generalization of SUSY with first-order supercharges and Higher order SUSY with second order supercharges - are combined for a class of 2-dim quantum models, which {\it are not amenable} to separation of variables. The appropriate classical limit of quantum systems allows us to construct SUSY-extensions of original classical scalar Hamiltonians. Special emphasis is placed on the symmetry properties of the models thus obtained - the explicit expressions of quantum symmetry operators and of classical integrals of motion are given for all (scalar and matrix) components of SUSY-extensions. Using Grassmanian variables, the symmetry operators and classical integrals of motion are written in a unique form for the whole Superhamiltonian. The links of the approach to the classical Hamilton-Jacobi method for related "flipped" potentials are established.

hep-th↗
arXiv2005

Quantum oscillations of self-dual Abrikosov-Nielsen-Olesen vortices

The mass shift induced by one-loop quantum fluctuations on self-dual ANO vortices is computed using heat kernel/generalized zeta function regularization methods. The quantum masses of super-imposed multi-vortices with vorticity lower than five are given. The case of two separate vortices with a quantum of magnetic flux is also discussed.

hep-th↗