The Low Lying Energy-Momentum Spectrum for the Lattice Four-Fermi Model

We obtain the low-lying energy-momentum spectrum for the imaginary-time lattice-Fermi or Gross-Neveu model in $d+1$ space-time dimensions ($d=1,2,3$) and N-component fermions. Let 0<\κ\ 0 be the hopping parameter,\λ>0 the four-fermion coupling, $m>0$ the bare fermion mass and take\× s spin matrices ($s=2,4$). Our analysis of the one and the-particle spectrum is based on spectral representation for suitable two- and-fermion correlations. The one-particle energy-momentum spectrum is obtained and is manifested by /2 isolated and identical dispersion, and the mass of particles has asymptotic value order -ln\κ. The of two-particle bound states above or below the two-particle band on whether Gaussian domination does hold or does not, respectively.-particle bound states emerge from solutions to a lattice Bethe-Salpeter, in a ladder approximation. Within this approximation, the(/2-1)/4 identical bound states have(\κ⁰) binding energies at zero system momentum and their are all equal, with value \≈ -2 ln \κ. Our results can be to the complete model as the Bethe-Salpeter kernel exhibits good decay.