Formfactor perturbation expansions and confinement in the Ising field theory

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 the 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 wavefunctions of the compound particles, leading to multi-fermion corrections to their masses M n ( h ) in higher orders in h . We describe a perturbative procedure, which allows us to account for 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 arises from the regular correction to the kernel of the Bethe–Salpeter equation.