Quantization of the localized solutions in two-dimensional field theories of massive fermions
Phys. Rev. D 12, 3880 – Published 15 December, 1975
DOI: https://doi.org/10.1103/PhysRevD.12.3880
Abstract
Using the semiclassical functional method developed by Dashen, Hasslacher, and Neveu, the classical localized solutions for the bound states of massive fermions in two-dimensional field theories are quantized. The mass spectra of the bound states are then obtained. For the massive Gross-Neveu model, the mass spectrum agrees with what has been found by Dashen et al. for the massless Gross-Neveu model where fermions acquire mass through dynamical symmetry breaking. For a theory of massive fermions with scalar as well as pseudoscalar Fermi interactions, the mass spectrum is found to be very similar to that for the doublet in the sine-Gordon equation. In fact, under certain conditions they become identical.