An operator expansion for integrable quantum field theories

TL;DR

This paper introduces a series expansion for observables in integrable quantum field theories in 1+1 dimensions, providing new insights into their structure and symmetries, and connecting with deformation methods like warped convolution.

Contribution

It establishes a novel series expansion for local observables in integrable models, independent of localization, and explores its relation to deformation techniques such as warped convolution.

Findings

The expansion is independent of localization properties.

Analysis of the expansion's behavior under space-time symmetries.

Clarification of relations with deformation methods like warped convolution.

Abstract

A large class of quantum field theories on 1+1 dimensional Minkowski space, namely, certain integrable models, has recently been constructed rigorously by Lechner. However, the construction is very abstract and the concrete form of local observables in these models remains largely unknown. Aiming for more insight into their structure, we establish a series expansion for observables, similar but not identical to the well-known form factor expansion. This expansion will be the basis for a characterization and explicit construction of local observables, to be discussed elsewhere. Here, we establish the expansion independent of the localization aspect, and analyze its behavior under space-time symmetries. We also clarify relations with deformation methods in quantum field theory, specifically, with the warped convolution in the sense of Buchholz and Summers.