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 field 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 find a formula for the one-loop kink mass shift that depends only on the part of the energy density with no field 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 $\lambda(\phi)_2^4$ models. The quantum corrections of the sG-soliton and $\lambda(\phi^4)_2$-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 $\phi^6$ models, is analyzed. The main virtue of our procedure is its versatility: it can be applied to practically any type of relativistic scalar field models supporting kinks.Comment: 35 pages, 6 figures, to be published in Nuclear Physics

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.Comment: 25 pages, 18 figure

Kink fluctuation asymptotics and zero modes

In this paper we propose a refinement of the heat kernel/zeta function treatment of kink quantum fluctuations in scalar field theory, further analyzing the existence and implications of a zero energy fluctuation mode. Improved understanding of the interplay between zero modes and the kink heat kernel expansion delivers asymptotic estimations of one-loop kink mass shifts with remarkably higher precision than previously obtained by means of the standard Gilkey-DeWitt heat kernel expansion.Comment: 21 pages, 8 figures, to be published in The European Physical Journal

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 non-linear non-dispersive waves points to variations in shape.Comment: 21 pages, 15 figures. To appear in Physica D: Nonlinear Phenomen

On the semiclassical mass of S2{\mathbb S}^2-kinks

One-loop mass shifts to the classical masses of stable kinks arising in a massive non-linear ${\mathbb S}^2$-sigma model are computed. Ultraviolet divergences are controlled using the heat kernel/zeta function regularization method. A comparison between the results achieved from exact and high-temperature asymptotic heat traces is analyzed in depth.Comment: RevTex file, 15 pages, 2 figures. Version to appear in Journal of Physics

The Kink variety in systems of two coupled scalar fields in two space-time dimensions

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.Comment: 12 pages, 5 figures. To appear in Phys. Rev.

Generalized MSTB Models: Structure and kink varieties

In this paper we describe the structure of a class of two-component scalar field models in a (1+1) Minkowskian space-time which generalize the well-known Montonen-Sarker-Trullinger-Bishop -hence MSTB- model. This class includes all the field models whose static field equations are equivalent to the Newton equations of two-dimensional type I Liouville mechanical systems with a discrete set of instability points. We offer a systematic procedure to characterize these models and to identify the solitary wave or kink solutions as homoclinic or heteroclinic trajectories in the analogous mechanical system. This procedure is applied to a one-parametric family of generalized MSTB models with a degree-eight polynomial as potential energy density.Comment: 46 pages, 18 figures, corrected typo