---
abstract: 'This paper investigates the relationship between algebraic quantum field theories and factorization algebras on globally hyperbolic Lorentzian manifolds. Functorial constructions that map between these two types of theories in both directions are developed under certain natural hypotheses, including suitable variants of the local constancy and descent axioms. The main result is an equivalence theorem between (Cauchy constant and additive) algebraic quantum field theories and (Cauchy constant, additive and time-orderable) prefactorization algebras. A concept of $\ast$-involution for the latter class of prefactorization algebras is introduced via transfer. This involves Cauchy constancy explicitly and does not extend to generic (time-orderable) prefactorization algebras.'
date: September 2019
title: |
    Model-independent comparison between factorization algebras\
    and algebraic quantum field theory on Lorentzian manifolds 
---

#### Report no.: {#report-no. .unnumbered}

ZMP-HH/19-6, Hamburger Beiträge zur Mathematik Nr. 781

#### Keywords: {#keywords .unnumbered}

algebraic quantum field theory, factorization algebras, Lorentzian geometry

#### MSC 2010: {#msc-2010 .unnumbered}

81Txx, 53C50

\[sec:intro\]Introduction and summary
=====================================

Factorization algebras and algebraic quantum field theory are two mathematical frameworks to axiomatize the algebraic structure of observables in a quantum field theory. While from a superficial point of view these two approaches look similar, there are subtle differences. A prefactorization algebra $\FFF$ assigns 