Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2007-01-26
Physics
High Energy Physics
High Energy Physics - Theory
4 pages, no figures
Scientific paper
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 $\kappa>0$ be the hopping parameter, $\lambda>0$ the four-fermion coupling and $M>0$ denote the fermion mass; and take $s\times s$ spin matrices, $s=2,4$. We work in the $\kappa\ll 1$ regime. 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 $-\ln\kappa$. 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. Two-particle bound states emerge from solutions to a lattice Bethe-Salpeter equation, in a ladder approximation. Within this approximation, the $sN(sN/2-1)/4$ identical bound states have ${\cal O}(\kappa^0)$ binding energies at zero system momentum and their masses are all equal, with value $\approx -2\ln\kappa$. Our results can be validated to the complete model as the Bethe-Salpeter kernel exhibits good decay properties.
da Veiga Paulo A. Faria
dos Anjos Petrus H. R.
No associations
LandOfFree
The low-lying energy-momentum spectrum for the four-Fermi model on a lattice does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with The low-lying energy-momentum spectrum for the four-Fermi model on a lattice, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The low-lying energy-momentum spectrum for the four-Fermi model on a lattice will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-493640