# Algebraic field theory operads and linear quantization

September 14, 2018

We generalize the operadic approach to algebraic quantum field theory
[arXiv:1709.08657] to a broader class of field theories whose observables on a
spacetime are algebras over any single-colored operad. A novel feature of our
framework is that it gives rise to adjunctions between different types of field
theories. As an interesting example, we study an adjunction whose left adjoint
describes the quantization of linear field theories. We also develop a derived
version of the linear quantization adjunction for chain complex valued field
theories, which in particular defines a homotopically meaningful quantization
prescription for linear gauge theories.

Keywords:

algebraic quantum field theory, locally covariant quantum field theory, colored operads, universal constructions, Gauge theory, model categories