arXiv subjects

A. C. R. Mendes

Publications and source records attributed to A. C. R. Mendes.

At least 19 recordsLinked to original sources

arXiv2018

Hořava-Lifshitz cosmological models in noncommutative space-times

In this work, we will analyze a noncommutative (NC) version of the Friedmann-Robert-Walker cosmological models within the gravitational Hořava-Lifshitz theory. The matter content of the models is described by a perfect fluid and the constant curvature of the spatial sections may be positive, negative or zero. In order to obtain this theory, we will use the Faddeev-Jackiw symplectic formalism to introduce, naturally, space-time noncommutativity inside the equations that provide the dynamics of the theory. We will investigate, in details, the classical field equations of a particular version of the NC models. The equations will be modified, with respect to the commutative ones, by the introduction of a NC parameter. We will demonstrate that various NC models, with different types of matter and spatial constant curvatures, show several interesting and new results relative to the corresponding commutative ones. We will pay special attention to some cases, where the NC model predicts a scale factor accelerated expansion, which may describe the current state of our Universe.

gr-qc↗

arXiv2014

Noncommutative analysis in a curved phase-space and coherent states quantization

In this work we have shown precisely that the curvature of a 2-sphere introduces quantum features in the system through the introduction of the noncommutative (NC) parameter that appeared naturally via equations of motion. To obtain this result we used the fact that quantum mechanics can be understood as a NC symplectic geometry, which generalized the standard description of classical mechanics as a symplectic geometry. In this work, we have also analyzed the dynamics of the model of a free particle over a 2-sphere in a NC phase-space. Besides, we have shown the solution of the equations of motion allows one to show the equivalence between the movement of the particle physical degrees of freedom upon a 2-sphere and the one described by a central field. We have considered the effective force felt by the particle as being caused by the curvature of the space. We have analyzed the NC Poisson algebra of classical observables in order to obtain the NC corrections to Newton's second law. We have demonstrated precisely that the curvature of the space acted as an effective potential for a free particle in a flat phase-space. Besides, through NC coherent states quantization we have obtained the Green function of the theory. The result have confirmed that we have an UV cutoff for large momenta in the NC kernel. We have also discussed the relation between affine connection and Dirac brackets, as they describe the proper evolution of the model over the surface of constraints in the Lagrangian and Hamiltonian formalisms, respectively. As an application, we have treated the so-called \textit{Zitterbewegung} of the Dirac electron. Since it is assumed to be an observable effect, then we have traced its physical origin by assuming that the electron has an internal structure.

hep-th↗

arXiv2013

Hidden symmetries in the two-dimensional isotropic antiferromagnet

We discuss the two-dimensional isotropic antiferromagnet in the framework of gauge invariance. Gauge invariance is one of the most subtle useful concepts in theoretical physics, since it allows one to describe the time evolution of complex physical systesm in arbitrary sequences of reference frames. All theories of the fundamental interactions rely on gauge invariance. In Dirac's approach, the two-dimensional isotropic antiferromagnet is subject to second class constraints, which are independent of the Hamiltonian symmetries and can be used to eliminate certain canonical variables from the theory. We have used the symplectic embedding formalism developed by a few of us to make the system under study gauge-invariant. After carrying out the embedding and Dirac analysis, we systematically show how second class constraints can generate hidden symmetries. We obtain the invariant second-order Lagrangian and the gauge-invariant model Hamiltonian. Finally, for a particular choice of factor ordering, we derive the functional Schrödinger equations for the original Hamiltonian and for the first class Hamiltonian and show them to be identical, which justifies our choice of factor ordering.

hep-th↗

arXiv2012

Obtaining gauge invariant actions via symplectic embedding formalism

The concept of gauge invariance is one of the most subtle and useful concepts in modern theoretical physics. It is one of the Standard Model cornerstones. The main benefit due to the gauge invariance is that it can permit the comprehension of difficult systems in physics with an arbitrary choice of a reference frame at every instant of time. It is the objective of this work to show a path of obtaining gauge invariant theories from non-invariant ones. Both are named also as first- and second-class theories respectively, obeying Dirac's formalism. Namely, it is very important to understand why it is always desirable to have a bridge between gauge invariant and non-invariant theories. Once established, this kind of mapping between first-class (gauge invariant) and second-class systems, in Dirac's formalism can be considered as a sort of equivalence. This work describe this kind of equivalence obtaining a gauge invariant theory starting with a non-invariant one using the symplectic embedding formalism developed by some of us some years back. To illustrate the procedure it was analyzed both Abelian and non-Abelian theories. It was demonstrated that this method is more convenient than others. For example, it was shown exactly that this embedding method used here does not require any special modification to handle with non-Abelian systems.

hep-th↗

arXiv2011

Noncommutative cosmological models coupled to a perfect fluid and a cosmological constant

In this work we carry out a noncommutative analysis of several Friedmann-Robert-Walker models, coupled to different types of perfect fluids and in the presence of a cosmological constant. The classical field equations are modified, by the introduction of a shift operator, in order to introduce noncommutativity in these models. We notice that the noncommutative versions of these models show several relevant differences with respect to the correspondent commutative ones.

hep-th↗

arXiv2011

Lagrangian formulation for noncommutative nonlinear systems

In this work we use the well known formalism developed by Faddeev and Jackiw to introduce noncommutativity within two nonlinear systems, the SU(2) Skyrme and O(3) nonlinear sigma models. The final result is the Lagrangian formulations for the noncommutative versions of both models. The possibility of obtaining different noncommutative versions for these nonlinear systems is demonstrated.

hep-th↗

arXiv2010

Gauge invariance and dual equivalence of Abelian and non-Abelian actions via dual embedding formalism

The concept of gauge invariance can be considered one of the most subtle and useful concept in theoretical physics since it can permit the comprehension of difficult systems in physics with an arbitrary choice of a reference frame at every instant of time. It is always desirable to have a bridge between gauge invariant and noninvariant theories. Once established, this kind of mapping between first-class (gauge invariant) and second-class systems, in Dirac's formalism can be considered as a sort of duality. In this paper we investigate this "duality" obtaining a gauge invariant theory starting with a noninvariant one. We analyzed both Abelian and non-Abelian theories and the procedure used is the recent dual (also called symplectic) embedding formalism. We believe that this method is the most convenient one since it is not plagued by the ambiguity problems that torments BFFT and other iterative methods. We demonstrated exactly that this "dualization" method used here does not require any special modification to handle with non-Abelian systems, which is also a new result described in this paper. To prove the gauge invariance we used just the Dirac constraint technique. It is relevant to say here that, although this work is lengthy, the majority of the results presented here are new in the literature. The results that are not new were reproduced within a new perspective.

hep-th↗

arXiv2009

Obtaining non-Abelian field theories via Faddeev-Jackiw symplectic formalism

In this work we have shown that it is possible to construct non-Abelian field theories employing, in a systematic way, the Faddeev-Jackiw symplectic formalism. This approach follows two steps. In the first step, the original Abelian fields are modified in order to introduce the non-Abelian algebra. After that, the Faddeev-Jackiw method is implemented and the gauge symmetry relative to some non-Abelian symmetry group, is introduced through the zero-mode of the symplectic matrix. We construct the SU(2) and SU(2)xU(1) Yang-Mills theories having as starting point the U(1) Maxwell electromagnetic theory.

hep-th↗

arXiv2009

Eliminating the chiral anomaly via symplectic embedding approach

The quantization of the chiral Schwinger model $(χQED_{2})$ with one-parameter class Faddeevian regularization is hampered by the chiral anomaly, i.e., the Gauss law commutator exhibits Faddeev's anomaly. To overcome this kind of problem, we propose to eliminate this anomaly by embedding the theory through a new gauge-invariant formalism based on the enlargement of the phase space with the introduction of Wess-Zumino(WZ) fields and the symplectic approach. This process opens up a possibility to formulate different, but dynamically equivalent, gauge invariant versions for the model and also gives a geometrical interpretation to the arbitrariness presents on the BFFT and iterative conversion methods. Further, we observe that the elimination of the chiral anomaly imposes a condition on the chiral parameters present on the original model and on the WZ sector.

hep-th↗

arXiv2008

Duality considerations about the Maxwell-Podolsky theory through the symplectic embedding formalism and spectrum analysis

We find the dual equivalent (gauge invariant) version of the Maxwell theory in D=4 with a Proca-like mass term by using the symplectic embedding method. The dual theory obtained (Maxwell-Podolsky) includes a higher-order derivative term and preserve the gauge symmetry. We also furnish an investigation of the pole structure of the vector propagator by the residue matrix which considers the eventual existence of the negative-norm of the theory.

hep-th↗

arXiv2008

Radiation damping, noncommutativity and duality

In this work, our main objective is to construct a N=2 supersymmetric extension of the nonrelativistic $(2+1)$-dimensional model describing the radiation damping on the noncommutative plane with scalar (electric) and vector (magnetic) interactions by the N=2 superfield technique. We also introduce a dual equivalent action to the radiation damping one using the Noether procedure.

hep-th↗

arXiv2007

Duality through the symplectic embedding formalism

In this work we show that we can obtain dual equivalent actions following the symplectic formalism with the introduction of extra variables which enlarge the phase space. We show that the results are equal as the one obtained with the recently developed gauging iterative Noether dualization method (NDM). We believe that, with the arbitrariness property of the zero mode, the symplectic embedding method (SEM) is more profound since it can reveal a whole family of dual equivalent actions. We illustrate the method demonstrating that the gauge-invariance of the electromagnetic Maxwell Lagrangian broken by the introduction of an explicit mass term and a topological term can be restored to obtain the dual equivalent and gauge-invariant version of the theory.

hep-th↗

arXiv2007

The dual embedding method in D=3

Improving the beginning steps of a previous work, we settle the dual embedding method (DEM) as an alternative and efficient method for obtaining dual equivalent actions also in D=3. We show that we can obtain dual equivalent actions which were previously obtained in the literature using the gauging iterative Noether dualization method (NDM). We believe that, with the arbitrariness property of the zero mode, the DEM is more profound since it can reveal a whole family of dual equivalent actions. After a review of our previous work, we obtain the dual equivalent theory of the self-dual model minimally coupled to U(1) charged bosonic matter. The result confirms the one obtained previously which is important since it has the same structure that appears in the Abelian Higgs model with an anomalous magnetic interaction.

hep-th↗

arXiv2006

Lagrangian description of the radiation damping

We present a Lagrangian formalism to the dissipative system of a charge interacting with its own radiation field, which gives rise to the radiation damping \cite{Heitler}, by the indirect representation doubling the phase-space dimensions.

cond-mat.other↗

arXiv2005

Supersymmetrization of the Radiation Damping

We construct a supersymmetrized version of the model to the radiation damping \cite{03} introduced by the present authors \cite{ACWF}. We dicuss its symmetries and the corresponding conserved Noether charges. It is shown this supersymmetric version provides a supersymmetric generalization of the Galilei algebra obtained in \cite{ACWF}. We have shown that the supersymmetric action can be splited into dynamically independent external and internal sectors.

hep-th↗

arXiv2005

Noncommutative Metafluid Dynamics

In this paper we define a noncommutative (NC) Metafluid Dynamics \cite{Marmanis}. We applied the Dirac's quantization to the Metafluid Dynamics on NC spaces. First class constraints were found which are the same obtained in \cite{BJP}. The gauge covariant quantization of the non-linear equations of fields on noncommutative spaces were studied. We have found the extended Hamiltonian which leads to equations of motion in the gauge covariant form. In addition, we show that a particular transformation \cite{Djemai} on the usual classical phase space (CPS) leads to the same results as of the $\star$-deformation with $ν=0$. Besides, we will shown that an additional term is introduced into the dissipative force due the NC geometry. This is an interesting feature due to the NC nature induced into model.

hep-th↗

arXiv2005

A New Approach to Canonical Quantization of the Radiation Damping

Inspired in some works about quantization of dissipative systems, in particular of the damped harmonic oscillator\cite{MB,RB,12}, we consider the dissipative system of a charge interacting with its own radiation, which originates the radiation damping (RD). Using the indirect Lagrangian representation we obtained a Lagrangian formalism with a Chern-Simons-like term. A Hamiltonian analysis is also done, what leads to the quantization of the system.

hep-th↗

arXiv2001

Embedding Second Class Systems via Symplectic Gauge-invariant Formalism

In this paper we reformulate Abelian and non-Abelian noninvariant systems as gauge invariant theories using a new constraint conversion scheme, developed on the symplectic framework. This conversion method is not plagued by the ambiguity problem that torments the BFFT and iterative methods and also it seems more powerful since it does not require special modifications to handle with non-Abelian systems.

hep-th↗