English

Smooth 1-dimensional algebraic quantum field theories

Mathematical Physics 2021-10-28 v2 High Energy Physics - Theory Category Theory math.MP

Abstract

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, of smooth families of smooth AQFTs and of equivariant smooth AQFTs are constructed. The main open problems that arise in upgrading this approach to higher dimensions and gauge theories are identified and discussed.

Keywords

Cite

@article{arxiv.2010.13808,
  title  = {Smooth 1-dimensional algebraic quantum field theories},
  author = {Marco Benini and Marco Perin and Alexander Schenkel},
  journal= {arXiv preprint arXiv:2010.13808},
  year   = {2021}
}

Comments

34 pages - Accepted for publication in Annales Henri Poincar\'e

R2 v1 2026-06-23T19:39:50.223Z