The BRST quantization of the U(1) gauged model of FJ-type chiral boson for [Formula: see text] and [Formula: see text] are performed using the Batalin–Fradkin–Vilkovisky formalism. BFV formalism converts the second-class algebra into an effective first-class algebra with the help of auxiliary fields. Explicit expressions of the BRST charge, the involutive Hamiltonian, and the preserving BRST symmetry action are given and the full quantization has been carried through. For [Formula: see text], this Hamiltonian gives the gauge invariant Lagrangian including the well-known Wess–Zumino term, while for [Formula: see text] the corresponding Lagrangian has the additional new type of the Wess–Zumino term. The spectra in both cases have been analysed and the Wess–Zumino actions in terms of auxiliary fields are identified.
Cosmological perturbations: a new gauge-invariant approach