New model structures for Algebraic Quantum Field Theory

TL;DR

This paper introduces new Quillen model structures to better understand the homotopy theory of algebraic quantum field theories, expanding the foundational framework and providing a new operadic algebra extension model structure.

Contribution

It presents novel Quillen model structures and a new extension model structure on operadic algebras, enhancing the analysis of homotopical phenomena in quantum field theory.

Findings

New Quillen model structures for algebraic quantum field theories

A novel extension model structure on operadic algebras via Bousfield localization

Enhanced framework for detecting homotopical phenomena in quantum field theory

Abstract

In this paper we define and compare several new Quillen model structures which present the homotopy theory of algebraic quantum field theories. In this way, we expand foundational work of Benini et al. by providing a richer framework to detect and treat homotopical phenomena in quantum field theory. Our main technical tool is a new extension model structure on operadic algebras which is constructed via (right) Bousfield localization. We expect that this tool is useful in other contexts.