José A. Helayël-Neto

Non-minimal coupling to a Lorentz-violating background and topological implications

Abstract.The non-minimal coupling of fermions to a background responsible for the breaking of Lorentz symmetry is introduced in Dirac’s equation; the non-relativistic regime is contemplated, and the Pauli equation is used to show how an Aharonov-Casher phase may appear as a natural consequence of the Lorentz violation, once the particle is placed in a region where there is an electric field. Different ways of implementing the Lorentz breaking are presented and, in each case, we show how to relate the Aharonov-Casher phase to the particular components of the background vector or tensor that realizes the violation of Lorentz symmetry.

A comment on the topological phase for anti-particles in a Lorentz-violating environment

Abstract Recently, a scheme to analyse topological phases in quantum mechanics by means of the non-relativistic limit of fermions non-minimally coupled to a Lorentz-breaking background has been proposed. In this Letter, we show that the fixed background, responsible for the Lorentz-symmetry violation, may induce opposite Aharonov–Casher phases for a particle and its corresponding anti-particle. We then argue that such a difference may be used to investigate the asymmetry for particle/anti-particle as well as to propose bounds on the associated Lorentz-symmetry violating parameters.

Dimensional reduction of the Abelian Higgs Carroll-Field-Jackiw model

Abstract.Taking as a starting point a Lorentz non-invariant abelian Higgs model defined in 1 + 3 dimensions, we carry out its dimensional reduction to D = 1 + 2, obtaining a new planar model composed by a Maxwell-Chern-Simons-Proca gauge sector, a massive scalar sector, and a mixing term (involving the fixed background

Investigations in the Lee-Wick electrodynamics

v^{\mu}

Un-graviton corrections to the Schwarzschild black hole

) that imposes the Lorentz violation to the reduced model. The propagators of the scalar and massive gauge field are evaluated and the corresponding dispersion relations determined. Based on the poles of the propagators, a causality and unitarity analysis is carried out at tree level. We then show that the model is totally causal, stable and unitary.

Classical and tree-level approaches to gravitational deflection in higher-derivative gravity

We consider the Lee–Wick (LW) electrodynamics, i.e. the U(1) gauge theory where a (gauge-invariant) dimension-6 operator containing higher derivatives is added to the free Lagrangian of the U(1) sector. A quantum bound on the LW heavy particle mass is then estimated by computing the anomalous electron–magnetic moment in the context of the aforementioned model. This limit is not only within the allowed range estimated by LW, it is also of the same order as that considered in early investigations on the possible effects of the LW heavy particle in e-e+ elastic scattering. A comparative study between the LW and the Coulomb potentials is also done.

Finite field-energy and interparticle potential in logarithmic electrodynamics

Abstract We introduce an effective action smoothly extending the standard Einstein–Hilbert action to include un-gravity effects. The improved field equations are solved for the un-graviton corrected Schwarzschild geometry reproducing the Mureika result. This is an important test to confirm the original “guess” of the form of the un-Schwarzschild metric. Instead of working in the weak field approximation and “dressing” the Newtonian potential with un-gravitons, we solve the “effective Einstein equations” including all order un-gravity effects. An unexpected “bonus” of accounting un-gravity effects is the fractalisation of the event horizon. In the un-gravity dominated regime the event horizon thermodynamically behaves as fractal surface of dimensionality twice the scale dimension d U .

Remarks on nonlinear electrodynamics

Among the so-called classical tests of general relativity (GR), light bending has been confirmed with an accuracy that increases as times goes by. Here we study the gravitational deflection of photons within the framework of classical and semiclassical higher-derivative gravity (HDG) -- the only version of GR that is known up to now to be renormalizable along with its matter couplings. Since our computations are restricted to scales much below the Planck cut-off we need not be afraid of the massive spin-2 ghost that haunts HDG. An upper bound on the constant related to the

Upper bounds on the photon mass

R^2_{\mu \nu}

Chern-Simons Gravity with (Curvature)

-sector of the theory is then found by analyzing -- from a classical and semiclassical viewpoint -- the deflection angle of a photon passing by the Sun. This upper limit greatly improves that available in the literature.