Field theoretical derivation of L\"uscher's formula and calculation of finite volume form factors

TL;DR

This paper develops a systematic field theoretical approach to derive L"uscher's formula and compute finite volume corrections to energy levels and form factors, validated through perturbation theory in sinh-Gordon theory.

Contribution

It introduces a method to calculate finite volume energy levels and form factors from momentum space two-point functions, including leading exponential corrections.

Findings

Derived finite volume energy and form factor corrections.

Validated results with perturbation theory in sinh-Gordon model.

Achieved perfect agreement with theoretical predictions.

Abstract

We initiate a systematic method to calculate both the finite volume energy levels and form factors from the momentum space finite volume two-point function. By expanding the two point function in the volume we extracted the leading exponential volume correction both to the energy of a moving particle state and to the simplest non-diagonal form factor. The form factor corrections are given in terms of a regularized infinite volume 3-particle form factor and terms related to the L\"usher correction of the momentum quantization. We tested these results against second order Lagrangian and Hamiltonian perturbation theory in the sinh-Gordon theory and we obtained perfect agreement.