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A vector field coming from spontaneous Lorentz violation mechanism, namely Bumblebee model is analysed in a topological framework in a $(1+2)D$ Minkowski space-time. Taking a $(1+2)D$ nonlinear Bumblebee vector matter field dynamics where we include topological like Chern-Simons type terms, a vector version of a soliton state, or vortex was found. The Nielsen-Olesen procedure was used in order to derive a Lorentz-violation vector parameter which characterizes, via Spontaneous Symmetry Breaking mechanism, the non-trivial vacuum. We verify the stability of the model as much as the magnetic vortex, and noticed that the soliton modes with polarized direction generated can be associated with local anisotropy of vacuum energy. The vortex equations of motion and the asymptotic behaviour is presented. We have obtained that the effect of the Lorentz symmetry violation expressed by the a time-like Bumblebee vector field vacuum could be shown as kind of pulse at a fixed point $r_0$ in a limitless universe, or as a barrier at $r_0$ which can represent a boundary in the universe, if the Bumblebee vector field vacuum has space-like characteristic. We also analyse the spectrum via propagators where we note that the topological mass contributes as well to the dynamical mass poles. We obtain that the Chern-Simons type terms, in fact, indicates the "speed" of the field to saturate the asymptotic limit and that the vortex core can not be dimension zero., Comment: 12 pages, 6 figures

In this paper we construct and study a formulation of a chargeless complex vector matter field in a supersymmetric framework. To this aim we combine two no-chiral scalar superfields in order to take the vector component field to build the chargeless complex vector superpartner where the respective field strength transforms as matter fields by a global $U(1)$ gauge symmetry. To the aim to deal with consistent terms without breaking the global $U(1)$ symmetry it imposes a choice to the complex combination revealing a kind of symmetry between the choices and eliminate the extra degrees of freedom consistently with the supersymmetry. As the usual case the mass supersymmetric sector contributes as a complement to dynamics of the model. We obtain the equations of motion of the Proca's type field, for the chiral spinor fields and for the scalar field on the mass-shell which show the same mass as expected. This work establishes the firsts steps to extend the analysis of charged massive vector field in a supersymmetric scenario., Comment: 8 pages

Taking a full 3D nonlinear vector matter field dynamics, a vector version of a soliton state was found. The Nielsen-Olesen procedure was used in order to derive a Lorentz-violation vector parameter which characterizes, via Spontaneous Symmetry Breaking mechanism, the non-trivial vacuum. A stable vortex configuration is obtained, and although the Chern-Simons-type terms do not contribute to the value of the vortex core, the propagator analysis suggests us the possibility of a contribution to the size of the vortex core and to the growth of the field to achieve the asymptotic limit value with the distance., Comment: 9 pages, 1 figure, Revtex4 format

In this paper we study the nonlocal effects of noncommutative spacetime on simple physical systems. Our main point is the assumption that the noncommutative effects are consequences of a background field which generates a local spin structure. So, we reformulate some simple electrostatic models in the presence of a spin-deformation contribution to the geometry of the motion, and we obtain an interesting correlation amongst the deformed area vector, the 3D noncommutative effects and the usual spin vector given in quantum mechanics framework. Remarkably we can observe that a spin-orbit coupling term comes to light on the spatial sector of a potential wrote in terms of noncommutative coordinates what indicates that bound states are particular cases in this procedure. Concerning to confined or bounded particles in this noncommutative domain we verify that the kinetic energy is modified by a deformation factor. Finally, we discuss about perspectives., Comment: 14 pages, 1 figure

We consider a model with a charged vector field along with a Cremmer-Scherk-Kalb-Ramond (CSKR) matter field coupled to a U(1) gauge potential. We obtain a natural Lorentz symmetry violation due to the local U(1) spontaneous symmetry breaking mechanism triggered by the imaginary part of the vector matter. The choice of the unitary gauge leads to the decoupling of the gauge-KR sector from the Higgs-KR sector. The excitation spectrum is carefully analyzed and the physical modes are identified. We propose an identification of the neutral massive spin-1 Higgs-like field with the massive Z' boson of the so-called mirror matter models., Comment: 10 pages, no figures, revtex4, Preprint CBPF-NF-037/03

We introduce a basis for a bi-dimensional finite matrix calculus and a bi-dimensional finite matrix action principle. As an application, we analyze scalar and spinorial fields in $D=4n+2$ in this approach. We verify that to establish a bi-dimensional matrix action principle we have to define a Dirac-algebra-modified Lebniz rule. From the bi-dimensional equations of motion, we obtain a matrix holomorphic feature for massless matrix scalar and spinorial fields., Comment: 9 pages, LaTex, revised version