Albert C. R. Mendes

New bounds for Tsallis parameter in a noncommutative phase-space entropic gravity and nonextensive Friedmann equations

In this paper, we have analyzed the nonextensive Tsallis statistical mechanics in the light of Verlinde’s formalism. We have obtained, with the aid of a noncommutative phase–space entropic gravity, a new bound for Tsallis nonextensive (NE) parameter (TNP) that is clearly different from the ones present in the current literature. We derived the Friedmann equations in a NE scenario. We also obtained here a relation between the gravitational constant and the TNP.

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

Abstract In this Letter we construct non-Abelian field theories employing the Faddeev–Jackiw symplectic formalism. The original Abelian fields were modified in order to introduce the non-Abelian algebra. We construct the SU ( 2 ) and SU ( 2 ) ⊗ U ( 1 ) Yang–Mills theories having as starting point the U ( 1 ) Maxwell electromagnetic theory.

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. We believe that, with the arbitrariness property of the zero mode, the symplectic embedding method 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.

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

A bstractIn 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 show that the noncommutative versions of these models show several relevant differences with respect to the correspondent commutative ones.

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. 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.

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 Diracs 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 Diracs 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.

Symplectic embedding of a fluid dynamical model

A complete investigation of hidden symmetries present in the d-dimensional fluid dynamical model will be carried out. This will be done in the context of Wess-Zumino (WZ) extension of phase space by using the symplectic embedding formalism. As a consequence, a set of dynamically equivalent symmetries existent in fluid field theory will be discovered. Further, an interesting relation between the WZ symmetries with hidden symmetries (Bazeia D and Jackiw R 1998 Ann. Phys., NY 270 246 (Preprint hep-th/ 9803165); Jackiw R 2000 Preprint physics/0010042) will be performed. Indeed, the global status of the symmetries will be lifted to a local one.

QCD gauge symmetries through Faddeev-Jackiw symplectic method

A bstractThe interactions between gluons are important in theories such as quantum chromodynamics. Therefore, to rediscover new features of well known methods in order to investigate the SU(3) gauge group can be a new way to deal with Yang-Mills theories. In this work we analyzed YM theories through the well known Faddeev-Jackiw formalism for constrained systems. Besides, we showed precisely that having U(1) Maxwell electromagnetic theory as a starting point we can construct SU(3)-like and SU(3) ⨂ SU(2) ⨂ U(1) non-Abelian theories.

LAGRANGIAN FORMULATION FOR NONCOMMUTATIVE NONLINEAR SYSTEMS

In this work we study Lagrangian formulations for the noncommutative versions of the SU(2) Skyrme model and O(3) nonlinear sigma model. These formulations will be obtained using the Faddeev–Jackiw symplectic formalism. Other noncommutative Lagrangian formulations can be proposed and different noncommutative versions for these nonlinear systems can be obtained.

MOND and cosmological issues from entropic gravity and nonextensive thermostatistics correspondence

It is an old idea to realize Einsteins equations as a thermodynamical equation of state. Hence, to understand the actual role of the holographic screen is a very relevant issue. In this letter we have analyzed the entropy as a function of the holographic screen in some different scenarios and calculated a modified Newtons gravitational law for each one of them. We have also disclosed the modified Newtonian dynamics (MOND) from Verlindes ideas. Besides, we have calculated some cosmological elements using the same concepts.