A Noncommutative Note on the Antibracket Formalism

F. Vanderseypen

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arXiv · hep-th/9309080

A Noncommutative Note on the Antibracket Formalism

F. Vanderseypen

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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.

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F. Vanderseypen. 1993-09-14. A Noncommutative Note on the Antibracket Formalism. https://arxiv.org/abs/hep-th/9309080

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