Abstract In this article, we review the dynamics of charge carriers in graphene and related 2D systems from a quantum field theoretical point of view. By allowing the electromagnetic fields to propagate throughout space and constraining fermions to move on a 2D manifold, the effective theory of such systems becomes a non-local version of quantum electrodynamics (QED) dubbed in literature pseudo or reduced QED. We review some aspects of the theory assuming the coupling arbitrary in strength. In particular, we focus on the chiral symmetry breaking scenarios and the analytical structure of the fermion propagator in vacuum and under the influence of external agents like a heat bath, in the presence of a Chern-Simons term, anisotropy and in curved space. We briefly discuss the major advances and some new results on this field.

Abstract By combining the variational principle with Heisenberg uncertainty principle in an effective Hamiltonian for heavy flavored mesons, we introduce a framework to estimate masses and radii of these states from an analytical constraint. In a novel manner, a model for quark velocity and a model for quark momentum width are introduced. These kinematical model parameters are obtained as analytical functions of inter quark separation in heavy quarkonia. The values of such quark parameters are then used in the calculation of S-wave annihilation decay rates of c c ¯ and b b ¯. To test the accuracy of our technique we first calculate the spin averaged masses, scalar radii and annihilation decay rates of charmonium and bottomonium without and with relativistic corrections by solving the Schrödinger wave equation with the appropriate parametrization of the Song-Lin potential. The Schrödinger wave equation is solved numerically with the matrix Numerov method and we observe a good agreement with the experimental measurements and other theoretical calculations and extract strong running coupling constant for c c ¯ and b b ¯ systems. In non-relativistic settings, heavy meson spectra have been obtained and extended to rather higher excited states within our framework by using bare masses of c and b quarks which we have extracted from analysis of experimental data.

Abstract We study the generation of an electromagnetic current in monolayer graphene immersed in a weak perpendicular magnetic field and radiated with linearly polarized monochromatic light. Such a current emits Bremsstrahlung radiation with the same amplitude above and below the plane of the sample, in the latter case consistent with the small amount of light absorption in the material. This mechanism could be an important contribution for the reflexion of light phenomenon in graphene.

Resumen Estudiamos la generación de una corriente electromagnética en una monocapa de grafeno inmersa en un campo magnético débil perpendicular y radiada con luz monocromática. Esta corriente emite radiación de Bremsstrahlung con la misma amplitud por arriba y abajo del plano de la muestra, en el u ́ltimo caso consistente con la pequen ̃a cantidad de absorción de luz en el material. Este mecanismo puede ser una contribución importante para el fenómeno de reflexión de luz en grafeno.

The ambiguities associated with the lack of gauge invariance in the non-perturbative truncations of Schwinger-Dyson equations (SDEs) are a challenging problem which has not yet been resolved in a decisive fashion. Pursuing this aim, we study dynamical chiral symmetry breaking in quantum electrodynamics in three space-time dimensions (QED3). We investigate the gauge dependence of the chiral condensate both in the quenched and the unquenched versions of the theory and emphasize the importance of taking into account the gauge covariance properties of the fermion propagator as dictated by its Landau-Khalatnikov-Fradkin transformation (LKFT). We present numerical solutions of the SDE of the fermion propagator which respect Ward-Green-Takahashi identities (WGTI) and LKFT simultaneously. As a striking consequence, we obtain a practically gauge independent chiral condensate.