A Derivation of the Cyclic Form Factor Equation

TL;DR

This paper derives the cyclic form factor equation in quantum field theory using principles from quantum field theory and modular operator properties, applicable to any massive 1+1 dimensional relativistic QFT.

Contribution

It provides a novel derivation of the cyclic form factor equation from fundamental QFT principles, independent of integrability.

Findings

The cyclic form factor equation holds in all massive 1+1D relativistic QFTs.

The derivation uses Haag-Ruelle fields and the KMS property of modular operators.

The result is general and does not depend on the integrability of the theory.

Abstract

A derivation of the cyclic form factor equation from quantum field theoretical principles is given; form factors being the matrix elements of a field operator between scattering states. The scattering states are constructed from Haag-Ruelle type interpolating fields with support in a `comoving' Rindler spacetime. The cyclic form factor equation then arises from the KMS property of the modular operators Delta associated with the field algebras of these Rindler wedges. The derivation in particular shows that the equation holds in any massive 1+1 dim. relativistic QFT, regardless of its integrability.