A. Alonso Izquierdo

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.

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.

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

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

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.

One-loop kink mass shifts: A computational approach.

In this paper we develop a procedure to compute the one-loop quantum correction to the kink masses in generic (1+1)-dimensional one-component scalar eld theoretical models. The procedure uses the generalized zeta function regularization method helped by the Gilkey-de Witt asymptotic expansion of the heat function via Mellin’s transform. We nd a formula for the one-loop kink mass shift that depends only on the part of the energy density with no eld derivatives, evaluated by means of a symbolic software algorithm that automates the computation. The improved algorithm with respect to earlier work in this subject has been tested in the sine-Gordon and ( ) 4 models. The quantum corrections of the sG-soliton and ( 4 )2-kink masses have been estimated with a relative error of 0:00006% and 0:00007% respectively. Thereafter, the algorithm is applied to other models. In particular, an interesting one-parametric family of double sine-Gordon models interpolating between the ordinary sine-Gordon and a re-scaled sine-Gordon model is addressed. Another one-parametric family, in this case of 6 models, is analyzed. The main virtue of our procedure is its versatility: it can be applied to practically any type of relativistic scalar eld models supporting kinks.

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

Abstract 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 π 2 . The procedure for computing the semi-classical mass shifts is based on canonical quantization and heat kernel/zeta function regularization methods.

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.

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.