Perturbative algebraic quantum field theory and beyond

TL;DR

This paper reviews perturbative algebraic quantum field theory, a rigorous framework that combines algebraic axioms with perturbative methods to construct interacting quantum field models in various spacetime geometries.

Contribution

It introduces a comprehensive review of perturbative algebraic QFT, including its non-perturbative developments and applicability to arbitrary globally hyperbolic manifolds.

Findings

Framework successfully constructs interacting QFT models in four dimensions

Development of non-perturbative local nets of C*-algebras

Applicable to arbitrary globally hyperbolic spacetimes

Abstract

In this review, we summarize the main ideas of perturbative algebraic quantum field theory, which is a rigorous framework combining some of the Haag-Kastler axioms with perturbative methods involving formal power series. It allows for the construction of interacting QFT models in four spacetime dimensions and works on arbitrary globally hyperbolic manifolds. This approach has also led to the development of a non-perturbative construction of local nets of C*-algebras for interacting theories, which will also be discussed at the end of this review.