Effects of torsion on electromagnetic fields

Abstract

In this work, we investigate the effects of torsion on electromagnetic fields. As a model spacetime, endowed with both curvature and torsion, we choose a generalization of the cosmic string, the cosmic dislocation. Maxwell's equations in the spacetime of a cosmic dislocation are then solved, considering both the case of a static, uniform, charge distribution along the string, and the case of a constant current flowing through the string. We find that the torsion associated to the defect affects only the magnetic field whereas curvature affects both electric and magnetic fields. Moreover, the magnetic field is found to spiral up around the defect axis.

A comment on the analogous confinement of a neutral particle to a quantum dot via noninertial effects

“…By considering the presence of topological defects [56][57][58], we have that the presence of a topological defect related to a torsion, for instance a screw dislocation, can modify the electromagnetic field in the rest frame of the observers [58]. Thus, it should be interesting to study the influence of torsion, for instance a screw dislocation or a edge dislocation [56,57], on the field configuration induced by the noninertial effects of the Fermi-Walker reference frame, and on the bound states.…”

On noninertial effects inducing a confinement of a neutral particle to a hard-wall confining potential

“…An interesting topic of discussion should be the influence of torsion [20,55,56] on this noninertial system. It has been shown in [55] that the presence of torsion can modify the electromagnetic field in the rest frame of the observers, thus, the presence of torsion can provide new discussions about the confinement of the neutral particle to a quantum dot via noninertial effects.…”

Electron on a cylinder with topological defects in a homogeneous magnetic field

“…Saying that, we take into account (8), and then we have the gauge A Z = A z = BR sin (θ/C). Finally, the Schrödinger equation to be studied is…”

“…In condensed matter physics the Riemann-Cartan geometry provides the interpretation of the curvature and torsion tensors as the surface densities of the Frank and Burges vectors, respectively [4]. Such feature leaves to many applications as the investigation of the fluid flow and the formation of viscous fingering patterns on a two-dimensional conical background space [5], the determination of the self-energy of a single charge in the presence of either a continuous distribution of disclinations or a continuous distribution of dislocations [6], the quantum scattering of an electron by a topological defect called dispiration [7], the effects of torsion on electromagnetic fields [8], the Berry quantum phase [9] and geometric phases in graphitic cones [10], etc. Due to technological progress, the physics of curved two-dimensional quantum systems is of great interest too, both theoretically and experimentally [11].…”