# Derivation of BRST charge

1. Jul 28, 2008

### ismaili

I would like to derive the explicit formula of the BRST charge.
http://en.wikipedia.org/wiki/BRST_formalism
(Bottom of Wiki link, I copy the formula here)
$$Q = c^i\left(L_i - \frac{1}{2}f_{ij}{}^kb_jc_k\right)$$
where $$c$$ is the ghost field, and $$b$$ is the antighost field, $$L_i$$ is the gauge group generator.
Actually, in wiki's article, right above the formula of BRST charge, there is a Lagrangian. I tried to use Noether theorem to calculate the charge, but in vain. $$J^\mu_a\sim \frac{\partial\mathcal{L}}{\partial\psi_{,\mu}}\delta\psi_a$$, replacing the $$\psi$$ with the ghost $$c$$, I ends up with
$$J^0 = \dot{b}\,\delta c = \dot{b}\left(-\frac{1}{2}f_{ij}{}^kc^ic^j\right)$$ whose volume integral looks different as the correct answer.
In there anybody who can help me or give me some hints?
Many thanks!

Last edited: Jul 28, 2008