An alternative prescription for gauging Floreanini-Jackiw chiral bosons

We seek new couplings of chiral bosons to U(1) gauge fields. Lorentz covariance of the resulting constrained lagrangian is checked with the help of a procedure based in the first-order formalism of Faddeev and Jackiw. We find Harada's constraint and another local one not previously considered. We analyze the constraint structure and part of the spectrum of this second solution and show that it is equivalent to an explicitly covariant coupling of Siegel's chiral boson to gauge fields, which preserves chirality under gauge transformations.