Ghost number ($\mathrm{gh}(c)=1,\mathrm{gh}(\bar{c})=-1$)

The additive grading assigns ghost number $+1$ to $c$ and $-1$ to $\bar{c}$. Physical observables have ghost number zero. This grading is distinct from spin or the Adjoint representation.

For ghost term $-({\partial }^{\mu }\bar{c})\cdot D_{\mu }c$ and the current convention $\delta S=-\int ({\partial }_{\mu }\theta )j_G^{\mu }$, localize $\delta c=\theta c$, $\delta \bar{c}=-\theta \bar{c}$. The two differentiated parameters give this current. Its Noether charge grades ghosts by $+1$ and antighosts by $-1$, up to the corresponding overall generator normalization.