arXiv subjects
Publications and source records attributed to B. M. Pimentel.
In this work we discuss the natural appearance of the Generalized Brackets in systems with non-involutive (equivalent to second class) constraints in the Hamilton-Jacobi formalism. We show how a consistent geometric interpretation of the integrability conditions leads to the reduction of degrees of freedom of these systems and, as consequence, naturally defines a dynamics in a reduced phase space.
A new quantum approach is presented that can account for the description of small ferromagnetic particles magnetization tunneling. An estimate of the saturation value of an external applied magnetic field along the easy axis is obtained. An analytic expression for the tunneling factor in the absence of an external magnetic field is deduced from the present approach that also allows to obtain the crossover temperature characterizing the regime where tunneling is dominated by the quantum effects.
We give an action for the massless spinning particle in pseudoclassical mechanics by using grassmann variables. The constructed action is invariant under $τ$-reparametrizations, local SUSY and O(N) transformations. After quantization, for the special case N=2, we get an action which describes the spin 0, 1 particles and topological sectors of the massless DKP theory. A SUSY formulation of the given model is also explored.
In this work we study the electromagnetic field at Finite Temperature via the massless DKP formalism. The constraint analysis is performed and the partition function for the theory is constructed and computed. When it is specialized to the spin 1 sector we obtain the well-known result for the thermodynamic equilibrium of the electromagnetic field.
The recent introduced \textit{dressed coordinates} are studied in the path-integral approach. These coordinates are defined in the context of a harmonic oscillator linearly coupled to massless scalar field and, it is shown that in this model the dressed coordinates appear as a coordinate transformation preserving the path-integral functional measure. The analysis also generalizes the \textit{sum rules} established in a previous work.
In this work we analyze systems described by Lagrangians with higher order derivatives in the context of the Hamilton-Jacobi formalism for first order actions. Two different approaches are studied here: the first one is analogous to the description of theories with higher derivatives in the hamiltonian formalism according to [Sov. Phys. Journ. 26 (1983) 730; the second treats the case where degenerate coordinate are present, in an analogy to reference [Nucl. Phys. B 630 (2002) 509]. Several examples are analyzed where a comparison between both approaches is made.
We developed the formal connection of the field theoretical Bethe-Salpeter equation including the ladder approximation with its representation on the light-front for a bosonic model. We use the light-front Green's function for the N-particle system for two-particles plus N-2 intermediate bosons. We derived an infinite set of coupled hierarchy equations or iterated resolvent from which the Green's function can be calculated. These equations allow a consistent truncation of the light-front Fock-space. We show explicitly the represention of the covariant two-body T-matrix and bound state vertex in the light-front.
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.
Massless scalar and vector fields are coupled to Lyra geometry by means of Duffin-Kemmer-Petiau (DKP) theory. Using Schwinger Variational Principle, equations of motion, conservation laws and gauge symmetry are implemented. We find that the scalar field couples to the anholonomic part of the torsion tensor, and the gauge symmetry of the electromagnetic field is not breaking by the coupling with torsion.
We consider the problem of an harmonic oscillator coupled to a scalar field in the framework of recently introduced dressed coordinates. We compute all the probabilities associated with the decay process of an excited level of the oscillator. Instead of doing direct quantum mechanical calculations we establish some sum rules from which we infer the probabilities associated to the different decay processes of the oscillator. Thus, the sum rules allows to show that the transition probabilities between excited levels follow a binomial distribution.
We analyse systems described by first order actions using the Hamilton-Jacobi (HJ) formalism for singular systems. In this study we verify that generalized brackets appear in a natural way in HJ approach, showing us the existence of a symplectic structure in the phase spaces of this formalism.
We intend to analyse the constraint structure of Teleparallelism employing the Hamilton-Jacobi formalism for singular systems. This study is conducted without using an ADM 3+1 decomposition and without fixing time gauge condition. It can be verified that the field equations constitute an integrable system.
We investigate the conformal invariance of massless Duffin-Kemmer-Petiau theory coupled to riemannian space-times. We show that, as usual, in the minimal coupling procedure only the spin 1 sector of the theory -which corresponds to the electromagnetic field- is conformally invariant. We show also that the conformal invariance of the spin 0 sector can be naturally achieved by introducing a compensating term in the lagrangian. Such a procedure -besides not modifying the spin 1 sector- leads to the well-known conformal coupling between the scalar curvature and the massless Klein-Gordon-Fock field. Going beyond the riemannian spacetimes, we briefly discuss the effects of a nonvanishing torsion in the scalar case.
We study the regularization ambiguities in an exact renormalized (1+1)-dimensional field theory. We show a relation between the regularization ambiguities and the coupling parameters of the theory as well as their role in the implementation of a local gauge symmetry at quantum level.
A manifestly covariant treatment of the free quantum eletromagnetic field, in a linear covariant gauge, is implemented employing the Schwinger's Variational Principle and the B-field formalism. It is also discussed the abelian Proca's model as an example of a system without constraints.
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.
We prove the equivalence of many-gluon Green functions in Duffin-Kemmer-Petieu and Klein-Gordon-Fock statistical quantum field theories. The proof is based on the functional integral formulation for the statistical generating functional in a finite-temperature quantum field theory. As an illustration, we calculate one-loop polarization operators in both theories and show that their expressions indeed coincide.
We propose an approach which allows to construct and use a potential function written in terms of an angle variable to describe interacting spin systems. We show how this can be implemented in the Lipkin-Meshkov-Glick, here considered a paradigmatic spin model. It is shown how some features of the energy gap can be interpreted in terms of a spin tunneling. A discrete Wigner function is constructed for a symmetric combination of two states of the model and its time evolution is obtained. The physical information extracted from that function reinforces our description of phase oscillations in a potential.