Hamiltonian from the path integral for theories with gauge freedom

Henneaux.

The Hamiltonian form of the path integral for theories with a gauge freedom is reviewed along the lines developed by Batalin, Fradkin and Vilkovisky. The formalism, which can be applied to gauge theories with an open algebra without the need for auxiliary fields, heavily relies on the canonical formulation of the Becchi-Rouet-Stora transformation. This transformation appears here as a purely classical object associated with the remarkable classical structure of (first class) constrained Hamiltonian systems. The occurrence of multi-ghost interactions in the effective quantum action is naturally predicted. The formalism is also extended to “reducible” gauge theories, i.e., theories whose gauge transformations are not independent, within which scope the recently studied anti-symmetric gauge fields fall. Here again, the BRS transformation plays a key role.