We introduce a method to obtain deformed defects starting from a given scalar field theory which possesses defect solutions. The procedure allows the construction of infinitely many new theories that support defect solutions, analytically expressed in terms of the defects of the original theory. The method is general, valid for both topological and non-topological defects, and we show how it extends to quantum mechanics, and how it works when the scalar field couples to fermions. We illustrate the general procedure with several examples, which support kink-like or lump-like defects. PACS numbers: 11.27.+d, 11.30.Er, 11.30.Pb Defects play important role in modern developments of several branches of physics. They may have topological or non-topological profile, and in Field Theory the topological defects usually appear in models that support spontaneous symmetry breaking, with the best known examples being kinks and domain walls, vortices and strings, and monopoles [1]. Domain walls, for example, are used to describe phenomena having rather distinct energy scales, as in high energy physics [1,2] and in condensed matter [3].The defects that we investigate in this letter are topological or kink-like defects, and nontopological or lumplike defects. They appear in models involving a single real scalar field, and are characterized by their amplitude and width, the width being related to the region in space where the defect solution appreciably deviates from vacuum states of the system. Interesting models that support kink-like defects involve polynomial potentials like the φ 4 model, periodic potentials like the sineGordon model, and even the vacuumless potential recently considered in [4,5]. We shall investigate defects by examining their solutions and the corresponding energy densities, to provide quantitative profile for both topological and nontopological defects.We introduce a general procedure to create deformed defects, starting from a known solvable model in one spatial dimension. We start with topological defects, and we show below that the proposed scheme generates, for each given model having topological solutions, infinitely many new solvable models possessing deformed topological defects. We examine stability of kink-like defects, to extend the procedure to quantum mechanics. We also investigate lump-like defects, to generalize the procedure to both topological and non-topological defects. Finally, we couple the scalar field to fermions, to show how the procedure works for the Yukawa coupling.The interest in kink-like defects is directly related to the role of symmetry restoration in cosmology [1,2] and in condensed matter [3]. Also, they are particularly important in other scenarios, where they may induce interesting effects. A significant example concerns the behavior of fermions in the background of kink-like structures [6]. The main point here is that symmetry breaking induces an effective mass term for fermions. In the background of the kink-like structure the fermionic mass varies from negative to...

No abstract

We consider the massive vector N-component (λϕ 4 ) D theory in Euclidian space and, using an extended Matsubara formalism we perform a compactification on aThis allows us to treat jointly the effect of temperature and spatial confinement in the effective potential of the model, setting forth grounds for an analysis of phase transitions driven by temperature and spatial boundary. For d = 2, which corresponds to the heated system confined between two parallel planes (separation L), we obtain, in the large N limit at one-loop order, formulas for temperature-and boundary-dependent mass and coupling constant. The equation for the critical curve in the β × L plane is also derived.

The development of quantum theory on a torus has a long history, and can be traced back to the 1920s, with the attempts by Nordström, Kaluza and Klein to define a fourth spatial dimension with a finite size, being curved in the form of a torus, such that Einstein and Maxwell equations would be unified. Many developments were carried out considering cosmological problems in association with particles physics, leading to methods that are useful for areas of physics, in which size effects play an important role. This interest in finite size effect systems has been increasing rapidly over the last decades, due principally to experimental improvements. In this review, the foundations of compactified quantum field theory on a torus are presented in a unified way, in order to consider applications in particle and condensed matted physics. The theory on a torus Γ d D = (S 1 ) d × R D−d is developed from a Lie-group representation and c*-algebra formalisms. As a first application, the quantum field theory at finite temperature, in its real-and imaginary-time versions, is addressed by focussing on its topological structure, the torus Γ 1 4 . The toroidal quantum-field theory provides the basis for a consistent approach of spontaneous symmetry breaking driven by both temperature and spatial boundaries. Then the superconductivity in films, wires and grains are analyzed, leading to some results that are comparable with experiments. The Casimir effect is studied taking the electromagnetic and Dirac field on a torus. In this case, the method of analysis is based on a generalized Bogoliubov transformation, that separates the Green function into two parts: one is associated with the empty space-time, while the other describes the impact of compactification. This provides a natural procedure for calculating the renormalized energy-momentum tensor. Self interacting four-fermion systems, described by the Gross-Neveu and Nambu-Jona-Lasinio models, are considered. Then finite size effects on the hadronic phase structure are investigated, taking into account density and temperature. As a final application, effects of extra spatial dimensions are addressed, by developing a quantum electrodynamics in a five-dimensional space-time, where the fifth-dimension is compactified on a torus. The formalism, initially developed for particle physics, provides results compatible with other trials of probing the existence of extra-dimensions.

We extend a deformation prescription recently introduced and present some new soluble nonlinear problems for kinks and lumps. In particular, we show how to generate models which present the basic ingredients needed to give rise to dimension bubbles. Also, we show how to deform models which possess lumplike solutions, to get to new models that support kinklike solutions.