Faddeev-Jackiw formalism for a topological-like oscillator in planar dimensions

TL;DR

This paper applies the Faddeev-Jackiw symplectic formalism to analyze a two-dimensional harmonic oscillator coupled with electromagnetic and topological (Chern-Simons) terms, revealing insights into constrained systems with topological features.

Contribution

It introduces a novel application of the Faddeev-Jackiw formalism to a topological-like oscillator in planar dimensions, highlighting its effectiveness for constrained systems with topological terms.

Findings

Successful formulation of the oscillator within the symplectic framework

Identification of constraints arising from topological coupling

Potential implications for topological quantum systems

Abstract

The problem of a harmonic oscillator coupling to an electromagnetic potential plus a topological-like (Chern-Simons) massive term, in two-dimensional space, is studied in the light of the symplectic formalism proposed by Faddeev and Jackiw for constrained systems.