The Batalin-Vilkovisky cohomology of the spinning particle

Abstract

Abstract: We show that the axiom of Felder and Kazhdan [4] 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.