Finite volume corrections of non-diagonal form factors

TL;DR

This thesis investigates finite volume corrections to non-diagonal form factors in the scaling Lee-Yang model, demonstrating the equivalence of two approaches for calculating $$-terms and clarifying their formal derivation.

Contribution

It explicitly shows that $$-terms from bound state quantization can be derived from $F$-term integrals by contour modification, confirming their equivalence and advancing understanding of finite volume effects.

Findings

$$-terms from different methods are equivalent

Explicit calculation confirms the relation between $$-terms and $F$-term integrals

Clarifies the formal derivation of $F$-terms in integrable quantum field theories

Abstract

This thesis presents L\"uscher's $\mu$- and $F$-term corrections to volume dependence of non-diagonal finite volume form factors in the scaling Lee-Yang model. An explicit calculation proves the suspected relation that the $\mu$-terms known previously from bound state quantization can be obtained from the $F$-term integrals by modifying the contour of integration such that it picks up residues of appropriate poles in the integrand. The fact that these two different approaches for getting the $\mu$-terms give the same result underpins the formal derivation of the $F$-term in arXiv:1904.00492 which was not known until recently. In the meantime, the notions of integrable quantum field theories and those related to their treatment in finite volume are introduced to help understand the topic for readers not familiar with it.