Algebraic field theory operads and linear quantization

TL;DR

This paper extends the operadic framework for algebraic quantum field theories to include a wider class of theories, introducing adjunctions that facilitate the quantization process, especially for linear and gauge theories, with homotopical considerations.

Contribution

It generalizes the operadic approach to encompass all algebras over single-colored operads and introduces a novel adjunction framework for quantization, including homotopical aspects.

Findings

Established a broader operadic framework for field theories.

Developed an adjunction describing linear quantization.

Analyzed homotopical properties for gauge theories.

Abstract

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 analyze homotopical properties of the linear quantization adjunction for chain complex valued field theories, which leads to a homotopically meaningful quantization prescription for linear gauge theories.