B. M. Pimentel

Spinorial Field and Lyra Geometry

The Dirac field is studied in a Lyra space-time background by means of the classical Schwinger Variational Principle. We obtain the equations of motion, establish the conservation laws, and get a scale relation relating the energy-momentum and spin tensors. Such scale relation is an intrinsic property for matter fields in Lyra background.

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.

A Teoria de Duffin-Kemmer-Petiau

The theory of Duffin-Kemmer-Petiau is presented from a historical point of view, highlighting the ideas and analogies which led to its formal development, as well as to its algebra and general properties. Furthermore, some misunderstood concepts surrounding the massless limit, m = 0, as well as the equivalence between this formalism and the formalisms of Klein-Gordon-Fock and Proca, for free and minimal coupling cases, are exposed. Insofar the completion of this study with the richness of the possible phenomenological interactions that make the theory of Duffin-Kemmer-Petiau a source of inspiration and culture.

Variational Formulation for Quaternionic Quantum Mechanics

Abstract.A quaternionic version of Quantum Mechanics is constructed using the Schwinger’s formulation based on measurements and a Variational Principle. Commutation relations and evolution equations are provided, and the results are compared with other formulations.

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 that 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 one. Thus, in the light of the 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.

O Efeito Casimir em Teoria das Fontes

The aim of this work is to introduce the Schwinger interpretation to the Casimir phenomenon, associated with the construction of a quantum dynamics which effectively describes the interaction between macroscopic objects (sources) from the point of view of a scattering theory (S-Matrix) using as guide the phenomenological interaction in material means. With this intention lets study the imposition of bondary conditions to the real non-massive Klein-Gordon-Fock field in (1+1) dimensions in the operatorial formalism and in the funcional formalism. Once elucidated the functional method, we approach the problem using the Schwinger reading.

Schwinger quantum action principle

The Schwinger quantum action principle is a dynamic characterization of the transformation functions and is based on the algebraic structure derived from the kinematic analysis of the measurement processes at the quantum level. As such, this variational principle, allows to derive the canonical commutation relations in a

Teoria algébrica de processos da medida em sistemas quânticos

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 measurement symbol. Such concept was conceived by Julian S. Schwinger and constitutes a fundamental piece in his variational formalism and its several applications.

Scalar and Vector Massive Fields in Lyra's Manifold ∗

The problem of coupling between spin and torsion is analysed from a Lyra’s manifold background for scalar and vector massive fields using the Duffin-Kemmer-Petiau (DKP) theory. We found the propagation of the torsion is dynamical, and the minimal coupling of DKP field corresponds to a non-minimal coupling in the standard Klein-Gordon-Fock and Proca approaches. The origin of this difference in the couplings is discussed in terms of equivalence by surface terms.