The four-fermion interaction in D=2,3,4: a nonperturbative treatment

Abstract

A new nonperturbative approach is used to investigate the Gross-Neveu model of four fermion interaction in the space-time dimensions 2, 3 and 4, the number $N$ of inner degrees of freedom being a fixed integer. The spontaneous symmetry breaking is shown to exist in $D=2,3$ and the running coupling constant is calculated. The four dimensional theory seems to be trivial.

a minor correction: one more acknowledgement is added. Latex 2.09 file, 15 pages, no figures, accepted for publication to Int.J.Mod.Phys.A

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