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B. M. Pimentel

Publications and source records attributed to B. M. Pimentel.

At least 37 records · Page 2Linked to original sources
arXiv2018

Bopp-Podolsky black holes and the no-hair theorem

Bopp-Podolsky electrodynamics is generalized to curved space-times. The equations of motion are written for the case of static spherically symmetric black holes and their exterior solutions are analyzed using Bekenstein's method. It is shown the solutions split-up into two parts, namely a non-homogeneous (asymptotically massless) regime and a homogeneous (asymptotically massive) sector which is null outside the event horizon. In addition, in the simplest approach to Bopp-Podolsky black holes, the non-homogeneous solutions are found to be Maxwell's solutions leading to a Reissner-Nordström black hole. It is also demonstrated that the only exterior solution consistent with the weak and null energy conditions is the Maxwell's one. Thus, in light of energy conditions, it is concluded that only Maxwell modes propagate outside the horizon and, therefore, the no-hair theorem is satisfied in the case of Bopp-Podolsky fields in spherically symmetric space-times.

gr-qc↗
arXiv2018

The Gauged Thirring Model in Thermodynamic Equilibrium

We study the Gauged Thirring Model (also known as Kondo Model) in thermodynamic equilibrium using the Matsubara-Fradkin-Nakanishi formalism. In this formulation, both the temperature and the chemical potential are kept to be nonvanishing. Starting from the field equations, we write down the Dyson-Schwinger-Fradkin equations, the Ward-Fradkin-Takahashi identities, and expressions for the thermodynamical generating functional. We find the partition function of the theory and study some key features of its exact two-point Green Functions, including the Landau-Khalatnikov/Fradkin transformations and some limiting cases of interest as well. In particular, we show that we can recover results from both the Schwinger and the Thirring's models from the Kondo Model in thermodynamic equilibrium.

hep-th↗
arXiv2017

Scalar Quantum Electrodynamics via Duffin-Kemmer-Petiau Gauge Theory in the Heisenberg Picture:Vacuum Polarization

Scalar Quantum Electrodynamics is investigated in the Heisenberg picture via the Duffin-Kemmer-Petiau gauge theory. On this framework, a perturbative method is used to compute the vacuum polarization tensor and its corresponding induced current for the case of a charged scalar field in the presence of an external electromagnetic field. Charge renormalization is brought into discussion for the interpretation of the results for the vacuum polarization.

hep-th↗
arXiv2017

Normalizability analysis of the generalized quantum electrodynamics from the causal point of view

The causal perturbation theory is an axiomatic perturbative theory of the S-matrix. This formalism has as its essence the following axioms: causality, Lorentz invariance and asymptotic conditions. Any other property must be showed via the inductive method order-by-order and, of course, it depends on the particular physical model. In this work we shall study the normalizability of the generalized quantum electrodynamics in the framework of the causal approach. Furthermore, we analyse the implication of the gauge invariance onto the model and obtain the respective Ward-Takahashi-Fradkin identities.

hep-th↗
arXiv2017

de Broglie-Proca and Bopp-Podolsky massive photon gases in cosmology

We investigate the influence of massive photons on the evolution of the expanding universe. Two particular models for generalized electrodynamics are considered, namely de Broglie-Proca and Bopp-Podolsky electrodynamics. We obtain the equation of state (EOS) $P=P(\varepsilon)$ for each case using dispersion relations derived from both theories. The EOS are inputted into the Friedmann equations of a homogeneous and isotropic space-time to determine the cosmic scale factor $a(t)$. It is shown that the photon non-null mass does not significantly alter the result $a\propto t^{1/2}$ valid for a massless photon gas; this is true either in de Broglie-Proca's case (where the photon mass $m$ is extremely small) or in Bopp-Podolsky theory (for which $m$ is extremely large).

astro-ph.CO↗
arXiv2017

Hamilton-Jacobi analysis of the four dimensional BF model with cosmological term

In this work we perform the Hamilton-Jacobi constraint analysis of the four dimensional Background Field (BF) model with cosmological term. We obtain the complete set of involutive Hamiltonians that guarantee the integrability of the system and identify the reduced phase space. From the fundamental differential we recover the equations of motion and obtain the generators of the gauge and shift transformations.

hep-th↗
arXiv2016

Non-perturbative Solution to the Quantum Interaction Problem via Schwinger's Action Principle

The most realistic situations in quantum mechanics involve the interaction between two or more systems. In the most of reliable models, the form and structure of the interactions generate differential equations which are, in the most of cases, almost impossible to solve exactly. In this paper, using the Schwinger Quantum Action Principle, we found the time transformation function that solves exactly the harmonic oscillator interacting with a set of other harmonic coupled oscillators. In order to do it, we have introduced a new special set of creation and annihilation operators which leads directly to the \emph{dressed states} associated to the system, which are the real quantum states of the interacting \emph{\textquotedblleft field-particle\textquotedblright} system. To obtain the closed solution, it is introduced in the same foot a set of \emph{normal mode} creation and annihilation operators of the system related to the first ones by an orthogonal transformation. We find the eigenstates, amplitude transitions and the system spectra without any approximation. At last, we show that the Schwinger Variational Principle provides the solutions in a free representation way.

quant-ph↗
arXiv2016

Multipole Expansion in Generalized Electrodynamics

In this article we study some classical aspects of Podolsky Electrodynamics in the static regime. We develop the multipole expansion for the theory in both the electrostatic and the magnetostatic cases. We also address the problem of consistently truncating the infinite series associated with the several kinds of multipoles, yielding approximations for the static Podolskian electromagnetic field to any degree of precision required. Moreover, we apply the general theory of multipole expansion to some specific physical problems. In those problems we identify the first terms of the series with the monopole, dipole and quadrupole terms in the generalized theory. We also propose a situation in which Podolsky theory can be experimentally tested.

hep-th↗
arXiv2016

Algebraic Theory of Measurement Processes in Quantum Systems

Here we deal in a pedagogical way with an approach to construct an algebraic structure for the Quantum Mechanical measurement processes from the concept of \emph{Measurement Symbol}. Such concept was conceived by Julian S. Schwinger and constitutes a fundamental piece in his variational formalism and its several applications.

quant-ph↗
arXiv2016

Electromagnetic Field in Lyra Manifold: A First Order Approach

We discuss the coupling of the electromagnetic field with a curved and torsioned Lyra manifold using the Duffin-Kemmer-Petiau theory. We will show how to obtain the equations of motion and energy-momentum and spin density tensors by means of the Schwinger Variational Principle.

gr-qc↗
arXiv2015

Functional quantization of Generalized Scalar Duffin-Kemmer-Petiau Electrodynamics

The main goal of this work is to study systematically the quantum aspects of the interaction between scalar particles in the framework of Generalized Scalar Duffin-Kemmer-Petiau Electrodynamics (GSDKP). For this purpose the theory is quantized after a constraint analysis following Dirac's methodology by determining the Hamiltonian transition amplitude. In particular, the covariant transition amplitude is established in the generalized non-mixing Lorenz gauge. The complete Green's functions are obtained through functional methods and the theory's renormalizability is also detailed presented. Next, the radiative corrections for the Green's functions at $α$-order are computed; and, as it turns out, an unexpected $m_{P}$-dependent divergence on the DKP sector of the theory is found. Furthermore, in order to show the effectiveness of the renormalization procedure on the present theory, a diagrammatic discussion on the photon self-energy and vertex part at $α^{2}$-order are presented, where it is possible to observe contributions from the DKP self-energy function, and then analyse whether or not this novel divergence propagates to higher-order contributions. Lastly, an energy range where the theory is well defined: $m^{2}\ll k^{2}<m_{p}^{2}$ was also found by evaluating the effective coupling for the GSDKP.

hep-th↗
arXiv2015

Three-dimensional Background Field Gravity: A Hamilton-Jacobi analysis

We analyse the constraint structure of the Background Field model for three dimensional gravity including a cosmological term via the Hamilton-Jacobi formalism. We find the complete set of involutive Hamiltonians that assures the integrability of the system and calculate the characteristic equations of the system. We established the equivalence between these equations and the field equations and also obtain the generators of canonical and gauge transformations.

hep-th↗
arXiv2014

The Epstein-Glaser causal approach to the Light-Front QED$_{4}$. I: Free theory

In this work we present the study of light-front field theories in the realm of axiomatic theory. It is known that when one uses the light-cone gauge pathological poles $(k^{+}) ^{-n}$ arises, demanding a prescription to be employed in order to tame these ill-defined poles and to have correct Feynman integrals due to the lack of Wick rotation in such theories. In order to shed a new light on this long standing problem we present here a discussion based on the use rigorous mathematical machinery of distributions combined with physical concepts, such as causality, to show how to deal with these singular propagators in a general fashion without making use of any prescription. The first step of our development will consist in showing how analytic representation for propagators arises by requiring general physical properties in the framework of Wightman's formalism. From that we shall determine the equal-time (anti)commutation relations in the light-front form for the scalar, fermionic fields and for the dynamical components of the electromagnetic field. In conclusion, we introduce the Epstein-Glaser causal method in order to have a mathematical rigorous treatment of the free propagators of the theory, allowing us to discuss the general treatment for propagators of the type $(k^{+}) ^{-n}$. Moreover, we show that at given conditions our results reproduce known prescriptions in the literature.

hep-th↗
arXiv2014

The Epstein-Glaser causal approach to the Light-Front QED$_{4}$. II: Vacuum Polarization tensor

In this work we show how to construct the one-loop vacuum polarization for light-front QED$_{4}$ in the framework of the perturbative causal theory. Usually, in the canonical approach, it is considered for the fermionic propagator the so-called instantaneous term, but it is known in literature that this term is controversial because it can be omitted by computational reasons; for instance, by compensation or vanishing by dimensional regularization. In this work we propose a solution to this paradox. First, in the perturbative causal theory, it is shown that the fermionic propagator does not have instantaneous terms, and with this propagator we calculate the one-loop vacuum polarization, from the calculation it follows the same result as obtained by the standard approach, but without reclaiming any extra assumptions. Moreover, since the perturbative causal theory is defined in the distributional framework, we can also show the reason behind we obtaining the same result whether we consider or not the instantaneous fermionic propagator term.

hep-th↗
arXiv2014

Causal approach for the electron-positron scattering in Generalized Quantum Electrodynamics

In this paper we study the generalized electrodynamics contribution for the electron-positron scattering process, $e^{-}e^{+}\rightarrow e^{-}e^{+}$, the Bhabha scattering. Within the framework of the standard model, for energies larger when compared to the electron mass, we calculate the cross section expression for the scattering process. This quantity is usually calculated in the framework of the Maxwell electrodynamics and, by phenomenological reasons, corrected by a cut-off parameter. On the other hand, by considering the generalized electrodynamics instead of Maxwell's, we can show that the effects played by the Podolsky mass is actually a natural cut-off parameter for this scattering process. Furthermore, by means of experimental data of Bhabha scattering we will estimate its lower bound value. Nevertheless, in order to have a mathematically well defined description of our study we shall present our discussion in the framework of the Epstein-Glaser causal theory.

hep-th↗
arXiv2014

Construction of dynamical invariants for the time-dependent harmonic oscillator with a time-dependent driven force

We construct the linear and quadratic polynomial dynamical invariants for the classical and quantum time-dependent harmonic oscillator driven by a time-dependent force. To obtain them, we use exclusively the associated equations of motion for the system. We also find an algebraic relationship between the linear and quadratic invariants at the classical and quantum level.

math-ph↗
arXiv2014

Involutive constrained systems and Hamilton-Jacobi formalism

In this paper, we study singular systems with complete sets of involutive constraints. The aim is to establish, within the Hamilton-Jacobi theory, the relationship between the Frobenius' theorem, the infinitesimal canonical transformations generated by constraints in involution with the Poisson brackets, and the lagrangian point (gauge) transformations of physical systems.

hep-th↗