Ronni G. G. Amorim

Non-commutative geometry and symplectic field theory

In this work we study representations of the Poincare group defined over symplectic manifolds, deriving the Klein-Gordon and the Dirac equation in phase space. The formalism is associated with relativistic Wigner functions; the Noether theorem is derived in phase space and an interacting field, including a gauge field, approach is discussed.

The Noncommutative Harmonic Oscillator Based on Symplectic Representation of Galilei Group

We study symplectic unitary representations for the Galilei group and derive the Schrödinger equation in phase space. Our formalism is based on the noncommutative structure of the star product. Guided by group theoretical concepts, we construct a physically consistent phase-space theory in which each state is described by a quasi-probability amplitude associated with the Wigner function. As applications, we derive the Wigner functions for the 3D harmonic oscillator and the noncommutative oscillator in phase space.

On classical thermal stability of black holes with a dynamical extrinsic curvature

We study the deformation caused by the influence of extrinsic curvature on a vacuum spherically symmetric metric embedded in a five-dimensional bulk. In this sense, we investigate the produced black-holes and derive general characteristics such as their masses, horizons, singularities and thermal properties. As a test, we also study the bending of light near such black-holes analyzing the movement of a test particle and the modification caused by extrinsic curvature on its movement. Accordingly, using the asymptotically conformal flat condition for the extrinsic curvature, an analytical expansion of a set of n-scalar fields can be defined and we show that the corresponding black holes must be large and constrained in the range of allowed values −1/2 ≤ n ≤ 1.8. As a result, they are locally thermodynamically stable, but not globally preferred.

Hénon–Heiles interaction for hydrogen atom in phase space

Using elements of symmetry, as gauge invariance, several aspects of a Schrodinger equation represented in phase space are introduced and analyzed under physical basis. The hydrogen atom is explored in the same context. Then we add a Henon–Heiles potential to the hydrogen atom in order to explore chaotic features.

Stefan-Boltzmann Law and Casimir Effect for the Scalar Field in Phase Space at Finite Temperature

We use the scalar field constructed in phase space to analyze the analogous Stefan-Boltzmann law and Casimir effect, both of them at finite temperature. The temperature is introduced by Thermo Field Dynamics (TFD) formalism and the quantities are analyzed once projected in the space of coordinates. We show that using the framework of phase space it is possible to introduce a thermal energy which is related to temperature as it vanishes when the temperature tends to zero. In fact given such a correlation the formalism of TFD is equivalent when project is in momenta space when compared to coordinates space.

On Quasinormal Modes for Scalar Perturbations of Static Spherically Symmetric Black Holes in Nash Embedding Framework

In this paper we investigate scalar perturbations of black holes embedded in a five-dimensional bulk space. The quasinormal frequencies of such black holes are calculated using the third order of Wentzel, Kramers, and Brillouin (WKB) approximation for scalar perturbations. The high overtones of quasinormal modes indicate a resonant-like set of black holes suggesting a serious constraint of embedding models in five dimensions.

Determinação da Massa e Dados Orbitais de Exoplanetas pelo Método Doppler

Doppler method, also called radial velocities method, is a technique used in detecting of exoplanets. About 70% of known exoplanets were discovered using this technique. The Doppler method consist in determine spectral shifts of host star of exoplanet, which enable measurement of the variation of radial velocity of host star towards of Earth or away from Earth. This movement of host star around center of mass occurs due to the existence of exoplanet. In this work we present a pedagogical review of the Doppler method applied to detection of exoplanets. In this sense, we analyze theoretical elements of this technique and their application.

Elementos de geometria Riemaniana: Análise da esfera S 2

This article presents concepts of Riemannian geometry and apply them to a two-dimensional sphere, the sphere S2, which is the simplest Riemannian manifold. Thus this article is intended to give enough subsidies to undergraduate students of physics to understand such concepts of geometry in order to facilitate the study of the general relativity. Similarly, this article is suitable to high school teachers who want to use basics concepts of Riemannian geometry to talk about the progress made in the field. In this sense, we introduce the curvature and define the manifold S2, showing that its curvature is not zero. This illustrates the theoretical framework of general relativity and it shows how the familiar concepts in Euclidian geometry change when the geometry is expanded. As an example we show how the Pythagorean theorem is built on this manifold.

On the Symplectic Dirac Equation

Symplectic unitary representations for the Poincaré group are studied. The formalism is based on the noncommutative structure of the star–product, and using group theory approach as a guide, a consistent physical theory in phase space is constructed. The state of a quantum mechanics system is described by a quasi-probability amplitude that is in association with the Wigner function. In this context, we derive the Klein–Gordon and Dirac equations. As an application, we study the Dirac equation with electromagnetic interaction in phase space.

Função de Wigner-80 anos e as origens da geometria não-comutativa

The concept of noncommutative space originates from the Wigner formulation of quantum mechanics in phase space in 1932. In parallel, Heisenberg was the first to propose noncommutative commutation relations between the components of the position operator. Such a possibility was mathematically described by Snyder, studying representations of the (4+1)-De Sitter group. A synthesis of such works is the concept of noncommutative geometry, established with the Moyal product, that arises in the Wigner formalism. In addition, such noncommutativity is found in some limits of string theory, giving rise to the possibility of measurements of spatial noncommutativity in high-energy physics. In this work, we present a pedagogical review of physical theories in noncommutative spaces, from a historical perspective. We emphasize the theory of symmetry group representations in phase space, and point out two important, but not so well-known, aspects: (a) the notion of amplitude of probability and the representation of the Schrodinger equation in phase space (usually, the phase space representation of quantum mechanics is derived from the density matrix and the Liouville-von Neumann equation); and (b) a work of Dirac in 1930, where a formulation of quantum physics was introduced by the first time.