Quantization of the localized solutions in two-dimensional field theories of massive fermions

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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.