# Quantization of Lorentzian free BV theories: factorization algebra vs algebraic quantum field theory

Marco Benini, Giorgio Musante, Alexander Schenkel
December 05, 2022
We construct and compare two alternative quantizations, as a time-orderable prefactorization algebra and as an algebraic quantum field theory valued in cochain complexes, of a natural collection of free BV theories on the category of $m$-dimensional globally hyperbolic Lorentzian manifolds. Our comparison is realized as an explicit isomorphism of time-orderable prefactorization algebras. The key ingredients of our approach are the retarded and advanced Green's homotopies associated with free BV theories, which generalize retarded and advanced Green's operators to cochain complexes of linear differential operators.

Keywords:
factorization algebras, algebraic quantum field theories, homological methods in gauge theory, globally hyperbolic Lorentzian manifolds, Green hyperbolic operators