Abstract:
We obtain exact traveling-wave solutions of the coupled nonlinear partial differential equations that describe the dynamics of two classical scalar fields in 1+1 dimensions. The solutions are kinks interpolating between neighboring vacua. We compute the classical kink mass and show that it saturates a Bogomol'nyi-type bound. We also present exact traveling-wave solutions of a more general class of models. Examples include coupled $\phi^4$ and sine-Gordon models.

Abstract:
We study the presence of kinks in models described by two real scalar fields in bidimensional spacetime. We generate new two-field models, constructed from distinct but important one-field models, and we solve them with techniques that we introduce in the current work. We illustrate the results with several examples of current interest to high energy physics. 1. Introduction The presence of kinks and solitons in models described by real scalar fields is of direct interest to high energy physics [1, 2] and other areas of nonlinear science [3, 4]. To mention specific studies, in high energy physics kinks appear in very interesting systems introduced, for instance, in [5, 6]. In condensed matter one can investigate domain walls in magnetic systems [7, 8], and nonlinear excitations in Bose-Einstein condensates [9, 10], to quote just a few examples. In this work we focus on one-field and two-field models in spacetime dimensions. Two very interesting models described by a single real scalar field are known as the sine-Gordon and the models, engendering spontaneous symmetry breaking. The model is described by a fourth-order polynomial potential and supports kink-like solutions, whereas the sine-Gordon model is characterized by a nonpolynomial potential and supports not only solitons but also multisoliton and breather solutions. Fluctuations around the solitons and kinks, however, are governed by the and reflectionless Hamiltonians of a general family known from supersymmetric quantum mechanics [11]. Moreover, a rich family of nonpolynomial models with spontaneous symmetry breaking was proposed in [12]. The main feature of the family of kinks arising in this family is that the Hamiltonians governing the kink small fluctuations cover many of the remaining transparent SUSY Hamiltonians; see also [13]. We start with these one-field models, which are described by polynomial and nonpolynomial , and we then move on to the two-field models constructed from the previous ones. Our aim is to identify kink solutions in these new models, which in general is a very difficult endeavor, as Rajaraman [14] notices: “This already brings us to the stage where no general methods are available for obtaining all localized static solutions (kinks), given the field equations. However, some solutions, but by no means all, can be obtained for a class of such Lagrangians using a little trial and error.” In this work we develop a technique which generates two-component kink solutions for two-field models in a straight-forward while way avoiding the use of the trial and error method

Abstract:
We study the structure of the manifold of solitary waves in a particular three-component scalar field theoretical model in two-dimensional Minkowski space. These solitary waves involve one, two, three, four, six or seven lumps of energy.

Abstract:
We study the problem of existence of static spherically symmetric wormholes supported by the kink-like configuration of a scalar field. With this aim we consider a self-consistent, real, nonlinear, nonminimally coupled scalar field $\phi$ in general relativity with the symmetry-breaking potential $V(\phi)$ possessing two minima. We classify all possible field configurations ruling out those of them for which wormhole solutions are impossible. Field configurations admitting wormholes are investigated numerically. Such the configurations represent a spherical domain wall localized near the wormhole throat.

Abstract:
We carry a Monte Carlo study of the coupled two-scalar $\lambda\phi^2_1 \phi^2_2$ model in three dimensions. We find no trace of Inverse Symmetry Breaking in the region of negative $\lambda$'s for which the one-loop effective potential predicts this phenomenon. Moreover, for $\lambda$'s negative enough, but still in the stability region for the potential, one of the transitions turns out to be of first order, both for zero and finite temperature.

Abstract:
The intrinsically relativistic problem of spinless particles subject to a general mixing of vector and scalar kink-like potentials ($\sim \mathrm{tanh} ,\gamma x$) is investigated. The problem is mapped into the exactly solvable Surm-Liouville problem with the Rosen-Morse potential and exact bounded solutions for particles and antiparticles are found. The behaviour of the spectrum is discussed in some detail. An apparent paradox concerning the uncertainty principle is solved by recurring to the concept of effective Compton wavelength.

Abstract:
We discuss some classical and quantum properties of 2d gravity models involving metric and a scalar field. Different models are parametrized in terms of a scalar potential. We show that a general Liouville-type model with exponential potential and linear curvature coupling is renormalisable at the quantum level while a particular model (corresponding to D=2 graviton-dilaton string effective action and having a black hole solution) is finite. We use the condition of a ``split" Weyl symmetry to suggest possible expressions for the ``effective" action which includes the quantum anomaly term.

Abstract:
We clarify some issues related to the evaluation of the mean value of the energy-momentum tensor for quantum scalar fields coupled to the dilaton field in two-dimensional gravity. Because of this coupling, the energy-momentum tensor for the matter is not conserved and therefore it is not determined by the trace anomaly. We discuss different approximations for the calculation of the energy-momentum tensor and show how to obtain the correct amount of Hawking radiation. We also compute cosmological particle creation and quantum corrections to the Newtonian potential.

Abstract:
Thermal scalar radiation in two spacetime dimensions is treated within relativistic classical physics. Part I involves an inertial frame where are given the analogues both of Boltzmann's derivation of the Stefan-Boltzmann law and also Wien's derivation of the displacement theorem using the scaling of relativitic radiation theory. Next the spectrum of classical scalar zero-point radiation in an inertial frame is derived both from scale invariance and from Lorentz invariance. Part II involves the behavior of thermal radiation in a coordinate frame undergoing (relativistic) constant acceleration, a Rindler frame. The radiation normal modes in a Rindler frame are obtained. The classical zero-point radiation of inertial frames is transformed over to the coordinates of a Rindler frame. Although for zero-point radiation the two-field correlation function at different spatial points at a single time is the same between inertial and Rindler frames, the correlation function at two different times at a single Rindler spatial coordinate is different, and has a natural extension to non-zero temperature. The thermal spectrum in the Rindler frame is then transferred back to an inertial frame, giving the familar Planck spectrum.

Abstract:
We study the $\lambda\phi^4_{1+1}$ kink solion and the zero-mode contribution to the Kink soliton mass in regions beyond the semiclassical regime. The calculations are done in the non-trivial scaling region and where appropriate the results are compared with the continuum, semiclassical values. We show, as a function of parameter space, where the zero-mode contributions become significant.