# Smooth 1-dimensional algebraic quantum field theories

October 26, 2020

This paper proposes a refinement of the usual concept of algebraic quantum
field theories (AQFTs) to theories that are smooth in the sense that they
assign to every smooth family of spacetimes a smooth family of observable
algebras. Using stacks of categories, this proposal is realized concretely for
the simplest case of 1-dimensional spacetimes, leading to a stack of smooth
1-dimensional AQFTs. Concrete examples of smooth AQFTs and also of smooth
families of smooth AQFTs are constructed. The main open problems that arise in
generalizing these techniques to higher-dimensional AQFTs are identified and
discussed.

Keywords:

algebraic quantum field theory, stacks of categories, vertical geometry of fiber bundles, smoothly parametrized differential equations