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.