Quasi-classical Study of Form Factors in Finite Volume

TL;DR

This work develops a quasi-classical framework for finite-volume form factors in c<1 conformal field theories by marrying separation of variables with Baxter equations. It links the quantum problem to the classical finite-zone (finite-genus) KdV spectrum, utilizing Riemann-surface data, BA functions, and a detailed quasi-classical Q-function construction. The main result is a concrete quasi-classical expression for matrix elements that factorizes into a universal, operator-independent factor and a finite-dimensional integral over separated variables, with consistency checks showing agreement with infinite-volume Sine-Gordon form factors in the L→∞ limit. The approach highlights the role of vacuum-like contributions and suggests a pathway toward exact finite-volume form factors through a structured, radiatively interpretable framework.

Abstract

We construct the quasi-classical approximation of the form factors in finite volume using the separation of variables. The latter is closely related to the Baxter equation.