The Batalin, Fradkin, and Vilkovisky formalism for higher-order theories

<jats:p>The generalized Batalin, Fradkin, and Vilkovisky (BFV) formalism was developed as a method for determining the ghost structure for theories, such as gravity and supergravity, whose Hamiltonian formalism has constraints not related to a Lie algebra action. Previously, the classical dynamical content of the BFV description of Yang–Mills theory was investigated. There it was found that this approach had a homological interpretation, derived from the Lie algebra cohomology of the gauge group, which allowed one to understand the construction in terms of the Dirac approach to constrained systems. In this paper the dynamical consequences of the generalized BFV formalism are investigated. It is found that even though one no longer has a Lie algebra structure associated with the constraints, one can still develop a homology theory that reproduces the Dirac analysis and from which the generalized BFV formalism can be derived. Some of the consequences of this approach are discussed.</jats:p>