Bound States of Majorana Fermions in Semi-classical Approximation

We derive a semi-classical formula for computing the spectrum of bound states made of Majorana fermions in a generic non-integrable 2d quantum field theory with a set of degenerate vacua. We illustrate the application of the formula in a series of cases, including an asymmetric well potential where the spectra of bosons and fermions may have some curious features. We also discuss the merging of fermionic and bosonic spectra in the presence of supersymmetry. Finally, we use the semi-classical formula to analyse the evolution of the particle spectra in a class of non-integrable supersymmetry models.