Remarks on Dirac-like Monopole, Maxwell and Maxwell-Chern-Simons Electrodynamics in D=(2+1)

TL;DR

This paper investigates classical Maxwell and Maxwell-Chern-Simons electrodynamics in (2+1) dimensions, analyzing potentials, fields, monopoles, and quantum effects, revealing unique features like harmonic oscillator behavior and energy eigenvalues.

Contribution

It provides new explicit solutions, explores monopole effects, and discusses quantum implications in (2+1)D electrodynamics, highlighting novel phenomena not previously detailed.

Findings

Explicit solutions for potentials and fields in (2+1)D

Dirac-like monopole induces tangential electric fields

Charged particle dynamics resemble a harmonic oscillator with discrete energy shifts

Abstract

Classical Maxwell and Maxwell-Chern-Simons (MCS) Electrodynamics in (2+1)D are studied in some details. General expressions for the potential and fields are obtained for both models, and some particular cases are explicitly solved. Conceptual and technical difficulties arise, however, for accelerated charges. The propagation of electromagnetic signals is also studied and their reverberation is worked out and discussed. Furthermore, we show that a Dirac-like monopole yields a (static) tangential electric field. We also discuss some classical and quantum consequences of the field created by such a monopole when acting upon an usual electric charge. In particular, we show that at large distances, the dynamics of one single charged particle under the action of such a potential and a constant (external) magnetic field as well, reduces to that of one central harmonic oscillator, presenting, however, an interesting angular sector which admits energy-eigenvalues. Among other peculiarities, both sectors, the radial and the angular one, present non-vanishing energy-eigenvalues for their lowest level. Moreover, those associated to the angle are shown to respond to discrete shifts of such a variable. We also raise the question whether the formation of bound states is possible in the system.