# Strictification theorems for the homotopy time-slice axiom

August 08, 2022

It is proven that the homotopy time-slice axiom for many types of algebraic
quantum field theories (AQFTs) taking values in chain complexes can be
strictified. This includes the cases of Haag-Kastler-type AQFTs on a fixed
globally hyperbolic Lorentzian manifold (with or without time-like boundary),
locally covariant conformal AQFTs in two spacetime dimensions, locally
covariant AQFTs in one spacetime dimension, and the relative Cauchy evolution.
The strictification theorems established in this paper prove that, under
suitable hypotheses that hold true for the examples listed above, there exists
a Quillen equivalence between the model category of AQFTs satisfying the
homotopy time-slice axiom and the model category of AQFTs satisfying the usual
strict time-slice axiom.

Keywords:

algebraic quantum field theory, Gauge theory, homotopical algebra, chain complexes, operads, localizations