M. A. Gonzalez Leon

Generalized zeta functions and one-loop corrections to quantum kink masses

Abstract 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 P ( φ ) 2 systems with polynomial self-interactions.

One-loop corrections to classical masses of kink families

Abstract 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 role 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.

Kinks in a nonlinear massive sigma model.

We describe the kink solitary waves of a massive nonlinear sigma model with an S2 sphere as the target manifold. Our solutions form a moduli space of nonrelativistic solitary waves in the long wavelength limit of ferromagnetic linear spin chains.

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.

Semi-classical mass of quantum k-component topological kinks

Abstract 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.

N=2 supersymmetric kinks and real algebraic curves

Abstract The kinks of the (1+1)-dimensional Wess-Zumino model with polynomic superpotential are investigated and shown to be related to real algebraic curves.

Stability of kink defects in a deformed O(3) linear sigma model

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.

Kink manifolds in (1+1)-dimensional scalar field theory

The general structure of kink manifolds in (1 + 1)-dimensional complex scalar field theory is described by analysing three special models. New solitary waves are reported. Kink energy sum rules arise between different types of solitary waves.

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.

Changing shapes : Adiabatic dynamics of composite solitary waves

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 nonlinear non-dispersive waves points to variations in shape.