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

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