Minimal models of quantum homotopy Lie algebras via the BV-formalism

Abstract

Using the Batalin-Vilkovisky-formalism of mathematical physics, an explicit construction for the minimal model of a quantum L∞-algebra is given as a formal super integral. The approach taken herein to these formal integrals is axiomatic, and they can be approached using perturbation theory to obtain combinatorial formulae as shown in the Appendix. Additionally, there exists a canonical differential graded Lie algebra morphism mapping formal functions on homology to formal functions on the whole space. An inverse L∞-algebra morphism to this differential graded Lie algebra morphism is constructed as a formal super integral.