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We obtain the low-lying energy-momentum spectrum for the imaginary-time lattice four-Fermi or Gross- Neveu model in d + 1 space-time dimensions (d = 1, 2, 3) and with N-component fermions. Let 0 < ? 0 be the hopping parameter, ? > 0 the four-fermion coupling, m > 0 the bare fermion mass and take s × s spin matrices (s = 2, 4). Our analysis of the one and the two-particle spectrum is based on spectral representation for suitable two- and four-fermion correlations. The one-particle energy-momentum spectrum is obtained rigorously and is manifested by sN 2 isolated and identical dispersion curves, and the mass of particles has asymptotic value order ?ln ?. The existence of two-particle bound states above or below the two-particle band depends on whether Gaussian domination does hold or does not, respectively.
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