The observables of a perturbative algebraic quantum field theory form a factorization algebra

We demonstrate that perturbative algebraic QFT methods, as developed by Fredenhagen and Rejzner, naturally yields a factorization algebras of observables for a large class of Lorentzian theories. Along the way we carefully articulate cochain-level refinements of multilocal functionals, building upon results about the variational bicomplex, and we lift existing results about Epstein-Glaser renormalization to these multilocal differential forms, results which may be of independent interest.Comment: 42 page