Matrix elements of the operator T\bar{T} in integrable quantum field theory

TL;DR

This paper derives exact matrix elements of the Tar{T} operator in integrable quantum field theories, explicitly demonstrating the method in the Lee-Yang model, building on Zamolodchikov's identities.

Contribution

It introduces a high-energy factorization requirement to determine Tar{T} matrix elements exactly in integrable models, exemplified in the Lee-Yang model.

Findings

Exact matrix elements of Tar{T} obtained for integrable theories.

High-energy factorization condition enables precise calculations.

Explicit construction demonstrated in the Lee-Yang model.

Abstract

Recently A. Zamolodchikov obtained a series of identities for the expectation values of the composite operator T\bar{T} constructed from the components of the energy-momentum tensor in two-dimensional quantum field theory. We show that if the theory is integrable the addition of a requirement of factorization at high energies can lead to the exact determination of the generic matrix element of this operator on the asymptotic states. The construction is performed explicitly in the Lee-Yang model.