= Ghost Virasoro zero-mode convention
{title2=$L_0^{\mathrm{gh}}|0\rangle=0$}
With the <ghost oscillator vacuum>, one can define $L_0^{\mathrm{gh}}=\sum_{k>0}k(b_{-k}c_k+c_{-k}b_k)$ with vacuum eigenvalue zero. The corresponding <Virasoro algebra> contains a linear shift: $[L_m^{\mathrm{gh}},L_n^{\mathrm{gh}}]=(m-n)(L_{m+n}^{\mathrm{gh}}-\delta_{m+n,0})-\tfrac{26}{12}(m^3-m)\delta_{m+n,0}$. Shifting the zero mode by minus one removes the linear term but changes the stated vacuum eigenvalue. A <BRST charge> must use a consistent choice throughout.
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