Definition: Relative field space

${\mathfrak{F}}_W$ is the graded space of multiplets $(\gamma ,\varphi ,c,\bar{c},b)$ with $c\in {\mathfrak{g}}_W\otimes {\Lambda }^{\mathrm{odd}}$ and the other fields unrestricted smooth sections, together with antifields as above, $c^{\ast }$ being a smooth section over $W$. The antibracket (eq:antibracket) is the canonical one for this pairing and satisfies the graded Jacobi identity.