Strictification theorems for the homotopy time-slice axiom

TL;DR

This paper proves that the homotopy time-slice axiom in various algebraic quantum field theories can be replaced by a strict version, establishing a Quillen equivalence under certain conditions.

Contribution

It introduces strictification theorems for the homotopy time-slice axiom in AQFTs, linking homotopy and strict models via Quillen equivalences.

Findings

Homotopy time-slice axiom can be strictified in many AQFTs.

Existence of Quillen equivalence between homotopy and strict AQFTs.

Applicable to AQFTs on Lorentzian manifolds and conformal theories.

Abstract

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.