Cresus F. L. Godinho

Extending the D’alembert solution to space–time Modified Riemann–Liouville fractional wave equations

Abstract In the realm of complexity, it is argued that adequate modeling of TeV-physics demands an approach based on fractal operators and fractional calculus (FC). Non-local theories and memory effects are connected to complexity and the FC. The non-differentiable nature of the microscopic dynamics may be connected with time scales. Based on the Modified Riemann–Liouville definition of fractional derivatives, we have worked out explicit solutions to a fractional wave equation with suitable initial conditions to carefully understand the time evolution of classical fields with a fractional dynamics. First, by considering space–time partial fractional derivatives of the same order in time and space, a generalized fractional D’alembertian is introduced and by means of a transformation of variables to light-cone coordinates, an explicit analytical solution is obtained. To address the situation of different orders in the time and space derivatives, we adopt different approaches, as it will become clear throughout this paper. Aspects connected to Lorentz symmetry are analyzed in both approaches.

Normal ordering and boundary conditions for fermionic string coordinates

Abstract We build up normal ordered products for fermionic open string coordinates consistent with boundary conditions. The results are obtained considering the presence of antisymmetric tensor fields. We find a discontinuity of the normal ordered products at string endpoints even in the absence of the background. We discuss how the energy–momentum tensor also changes at the world-sheet boundary in such a way that the central charge keeps the standard value at string end points.

Gauge invariant actions for the noncommutative phase-space relativistic particle

Our main interest here is to analyze the gauge invariance issue concerning the noncommutative relativistic particle. Since the analysis of the constraint set from Dirac’s point of view classifies it as a second-class system, it is not a gauge theory. Hence, the objective here is to obtain gauge invariant actions linked to the original one. However, we have two starting points, meaning that firstly we will begin directly from the original action and, using the Noether procedure, we have obtained a specific dual (gauge invariant) action. Following another path, we will act towards the constraints so that we have carried out the conversion of second to first-class constraints through the Batalin–Fradkin–Fradkina–Tyutin formalism, obtaining the second gauge invariant Lagrangian.

On the role of a torsion-like field in a scenario for the Spin Hall Effect

Centro Brasileiro de Pesquisas F´isicas (CBPF),Rua Dr. Xavier Sigaud 150, Urca,22290-180, Rio de Janeiro, BrazilDecember 16, 2014Starting from an action that describes a Dirac fermion, we propose and analyze a model based ona low-relativistic Pauli equation coupled to a torsion-like term to study Spin Hall Effect (SHE). Wepoint out a very particular connection between the modified Pauli equation and the (SHE), wherewhat we refer to torsion as field playing an important role in the spin-orbit coupling process. In thisscenario, we present a proposal of a spin-type current, considering the tiny contributions of torsionin connection with geometrical properties of the material.

Fractional Canonical Quantization: a Parallel with Noncommutativity

Adopting a particular approach to fractional calculus, this paper sets out to build up a consistent extension of the Faddeev-Jackiw (or Symplectic) algorithm to carry out the quantization procedure of coarse-grained models in the standard canonical way. In our treatment, we shall work with the Modified Riemman Liouville (MRL) approach for fractional derivatives, where the chain rule is as efficient as it is in the standard differential calculus. We still present a case where we consider the situation of charged particles moving on a plane with velocity ṙ

The non-commutative U(N) Kalb-Ramond theory

\dot {r}

Constrained Systems in a Coarse-Grained Scenario

, subject to an external and intense magnetic field in a coarse-grained scenario. We propose an interesting parallelism with the noncommutative case.

Variational Procedure for Higher-Derivative Mechanical Models in a Fractional Integral Framework

Abstract We present the non-commutative extension of the U ( N ) Cremmer–Scherk–Kalb–Ramond theory, displaying its differential form and gauge structures. The Seiberg–Witten map of the model is also constructed up to 0( θ 2 ).