BRST physical-state constraints of an open string ($(L_0-1)|\Psi ⟩=L_{m>0}|\Psi ⟩=0$)

For a matter state tensored with the ghost oscillator vacuum, the BRST charge produces the independent ghost states $c_0|0⟩$ and $c_{-m}|0⟩$ with coefficients $(L_0-1)|\Psi ⟩$ and $L_m|\Psi ⟩$. Thus BRST closure is equivalent to $(L_0-1)|\Psi ⟩=0$ and $L_{m>0}|\Psi ⟩=0$ in this sector. It reproduces old covariant string quantization and the open bosonic string mass spectrum.