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Simple BRST quantization of general gauge models

It is shown that the BRST charge $Q$ for any gauge model with a Lie algebra symmetry may be decomposed as $$Q=\del+\del^†, \del^2=\del^{†2}=0, [\del, \del^†]_+=0$$ provided dynamical Lagrange multipliers are used but without introducing other matter variables in $\del$ than the gauge generators in $Q$. Furthermore, $\del$ is shown to have the form $\del=c^{†a}ϕ_a$ (or $ϕ'_ac^{†a}$) where $c^a$ are anticommuting expressions in the ghosts and Lagrange multipliers, and where the non-hermitian operators $ϕ_a$ satisfy the same Lie algebra as the original gauge generators. By means of a bigrading the BRST condition reduces to $\del|ph\hb=\del^†|ph\hb=0$ which is naturally solved by $c^a|ph\hb=ϕ_a|ph\hb=0$ (or $c^{†a}|ph\hb={ϕ'_a}^†|ph\hb=0$). The general solutions are shown to have a very simple form.