541 research outputs found
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 models. The
quantum corrections of the sG-soliton and -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 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 -kinks
One-loop mass shifts to the classical masses of stable kinks arising in a
massive non-linear -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
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