The low-lying energy-momentum spectrum for the four-Fermi model on a lattice
| dc.creator | Anjos, Petrus H. R. dos | |
| dc.creator | da Veiga, Paulo A. Faria | |
| dc.date | 2007-01-26 | |
| dc.date.accessioned | 2026-07-07T07:43:31Z | |
| dc.date.available | 2026-07-07T07:43:31Z | |
| dc.description | 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 $κ>0$ be the hopping parameter, $λ>0$ 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 $κ\ll 1$ 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 $-\lnκ$. 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 ${\cal O}(κ^0)$ binding energies at zero system momentum and their masses are all equal, with value $\approx -2\lnκ$. Our results can be validated to the complete model as the Bethe-Salpeter kernel exhibits good decay properties. | |
| dc.description | 4 pages, no figures | |
| dc.identifier | https://arxiv.org/abs/hep-th/0701251 | |
| dc.identifier | http://arxiv.org/abs/hep-th/0701251 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/122858 | |
| dc.subject | High Energy Physics - Theory | |
| dc.title | The low-lying energy-momentum spectrum for the four-Fermi model on a lattice | |
| dc.type | text |