New model structures for Algebraic 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.