We begin with a ``free'' gauge theory, described by a Lagrangian action , invariant under some gauge transformations
Equation (57) is fulfilled by hypothesis. The next one requires that the first-order deformation of the solution to the master equation, , is a cocycle of the ``free'' BRST differential . However, only cohomologically nontrivial solutions to (58) should be taken into account, as the BRST-exact ones can be eliminated by (in general nonlinear) field redefinitions. This means that pertains to the ghost number zero cohomological space of , , which is generically nonempty due to its isomorphism to the space of physical observables of the ``free'' theory. It has been shown in [39,40] (on behalf of the triviality of the antibracket map in the cohomology of the BRST differential) that there are no obstructions in finding solutions to the remaining equations, namely, ( 59), (60) and so on. However, the resulting interactions may be nonlocal, and there might even appear obstructions if one insists on their locality. The analysis of these obstructions can be done with the help of cohomological techniques. As it will be seen below, all the interactions in the case of the model under study turn out to be local.