Algebraic constructive quantum field theory: Integrable models and deformation techniques

TL;DR

This paper reviews algebraic methods for constructing quantum field theory models, focusing on Borchers triples, integrable models, and deformation techniques like warped convolution, to advance the understanding of QFT structures.

Contribution

It introduces a unified operator-algebraic framework for free, integrable, and deformed quantum field theories using Borchers triples and deformation methods.

Findings

Construction of free field theories from standard pairs

Inverse scattering method for integrable models in 2D

Warped convolution deformation of QFT models in arbitrary dimensions

Abstract

Several related operator-algebraic constructions for quantum field theory models on Minkowski spacetime are reviewed. The common theme of these constructions is that of a Borchers triple, capturing the structure of observables localized in a Rindler wedge. After reviewing the abstract setting, we discuss in this framework i) the construction of free field theories from standard pairs, ii) the inverse scattering construction of integrable QFT models on two-dimensional Minkowski space, and iii) the warped convolution deformation of QFT models in arbitrary dimension, inspired from non-commutative Minkowski space.