The Batalin-Vilkovisky formalism of the spinning particle

Abstract

We show that the axiom of Felder and Kazhdan on the vanishing of the cohomology groups in negative degree associated to solutions of the classical master equation in the Batalin-Vilkovisky formalism is violated by the spinning particle in a flat background coupled to D=1 supergravity. In this model, there are nontrivial cohomology groups in all negative degrees, regardless of the dimension of the spacetime in which the spinning particle is propagating.