The Moyal cohomology of the N=1 spinning particle

Abstract

The Batalin-Fradkin-Vilkovisky formalism studies a differential graded symplectic supermanifold whose cohomology vanishes in negative degree. This hypothesis is violated by the N=1 spinning particle arXiv:1605.04762; its cohomology is nontrivial in all negative degrees. Replacing the Poisson bracket by the Moyal bracket has the effect of eliminating these cohomology classes.

Many revisions and corrections from first version, and added discussion of relationship of these results to the BFV formalism. 13 pages