Quantum Field Theory for Homological Algebraists

The BV formalism in quantum field theory provides a homological theory of integration that can be used to compute path integrals. The present note is an overview of such ideas. Starting with a discussion of the combinatorial algorithms used by physicists to compute correlators, we motivate the structures involved in studying observables in BV theories via the finite dimensional case. In particular, we show that the quantum BV formalism recovers the same algorithms from structures manifestly arising from integration. We then discuss the infinite dimensional case.