Formfactor perturbation expansions and confinement in the Ising field theory

TL;DR

This paper develops a perturbative approach to analyze the particle spectrum in the two-dimensional Ising field theory under a weak magnetic field, incorporating multi-fermion effects and confinement phenomena.

Contribution

It introduces a formfactor perturbation expansion method that accounts for multi-fermion fluctuations and long-range confinement in the Ising field theory.

Findings

Derived integral representations for third-order multi-fermion mass corrections

Established a perturbative framework for formfactor expansions in confining theories

Provided insights into the particle spectrum modifications due to weak magnetic fields

Abstract

We study the particle spectrum M_n(h) in the two-dimensional ferromagnetic Ising field theory in a weak external magnetic field h. According to Wu and McCoy scenario of the weak confinement, pairs of fermions (domain walls) are coupled into bosonic kink-antikink bound states at small h>0. Fluctuations with more than two fermions also contribute to the wave functions of the compound particles, leading to the multi-fermion corrections to their masses M_n(h) in higher orders in h. We describe a perturbative procedure, which allows to account both multi-fermion fluctuations, and the long-range confining interaction between fermions, and leads to the formfactor expansions for the renormalized parameters of the model. We obtain integral representations for the third-order multi-fermion correction to the mass M_n(h), which arise from the regular correction to the kernel of the Bethe-Salpeter equation.