TL;DR
This paper explores vortex solutions in a modified (2+1)-dimensional electromagnetism theory replacing the Maxwell term with a Chern-Simons term, relevant for phenomena like the Quantum Hall Effect and superconductivity.
Contribution
It analyzes finite-energy vortex solutions in Chern-Simons modified electromagnetism coupled to scalar fields, both relativistically and non-relativistically.
Findings
Finite-energy vortex solutions exist in the Chern-Simons framework.
The solutions are applicable to Quantum Hall Effect and superconductivity models.
The study extends understanding of topological solitons in lower-dimensional gauge theories.
Abstract
In (2+1) dimensions, the Maxwell term can be replaced by the Chern-Simons three-form , yielding a novel type of `electromagnetism'. This has been proposed for studying the Quantum Hall Effect as well as High-Temperature Superconductivity. The gauge field can be coupled to a scalar field either relativistically or non-relativistically. In both cases, one admits finite-energy, vortex solutions.
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