$\mathfrak{g}$-Symplectic Orbits and a Solution of the BRST Consistency Condition

Abstract

For any Lie algebra $\mathfrak{g}$ we introduce the notion of $\mathfrak{g}$-symplectic structures and show that every orbit of a principal $G$-bundle carries a natural $\mathfrak{g}$-symplectic form and an associated momentum map induced by the Maurer–Cartan form on $G$. We apply this to the BRST bicomplex and show that the associated momentum map is a solution of the Wess–Zumino consistency condition for the anomaly.