From the BRST invariant Hamiltonian to the Field-Antifield Formalism

We study the relation between the lagrangian field-antifield formalism and the BRST invariant phase space formulation of gauge theories. Starting from the Batalin-Fradkin-Vilkovisky unitarized action, we demonstrate in a deductive way the equivalence of the phase space, and the lagrangian field-antifield partition functions for the case of irreducible first rank theories.