First order formalism for generalized vortices

Abstract This work develops a procedure to find classes of Lagrangian densities that describe generalizations of the Abelian Maxwell–Higgs, the Chern–Simons–Higgs and the Maxwell–Chern–Simons–Higgs models. The investigation focuses on the construction of models that support vortices that obey the stressless condition and lead to first order differential equations which are compatible with the equations of motion. The results induce the appearance of constraints that restrict the choice of the Lagrangian densities, but help us to introduce an auxiliary function that allows to calculate the energy without knowing the explicit form of the solutions.