TL;DR
This paper explores vortex solutions in systems lacking a vacuum state, using Maxwell and Chern-Simons dynamics, and introduces a first order formalism to analyze their properties and energy without explicit solutions.
Contribution
It presents a novel approach to find and analyze vortex solutions in vacuumless potentials using a first order formalism with Maxwell and Chern-Simons dynamics.
Findings
Vortex solutions have large tails but maintain well-defined magnetic flux.
Energy can be calculated without explicit solutions.
Solutions exhibit unique properties due to the absence of a vacuum state.
Abstract
We investigate the presence of vortex solutions in potentials without vacuum state. The study is conducted considering Maxwell and Chern-Simons dynamics. Also, we use a first order formalism that helps us to find the solutions and their respective electromagnetic fields and energy densities. As a bonus, we get to calculate the energy without knowing the explicit solutions. Even though the solutions present a large "tail" which goes far away from the origin, the magnetic flux remains a well defined topological invariant.
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