A Noncommutative Note on the Antibracket Formalism

Abstract

We introduce a noncommutative calculus on the odd-symplectic superspace $\scri$ of fields and antifields. To this end we have to extend $\scri$ to $\exscri$ by including an extra anticommuting field $η$. As a consequence we show that the commutator induced on $\exnice\times T^\star(\exnice)$ is proportional to the antibracket. The $Δ$-operator is an element of the quotient space of derivations twisted by the antibracket $A\der$ and $\der$. The natural measure on $\exscri$ is shown to be invariant under canonical transformations provided a certain 'wave equation' is satisfied.