FERMIONS WITH LONG-RANGE INTERACTION

A renormalization-group analysis combined with bosonization is perform ed for fermions interacting with repulsive long-range interaction of t he form V(R)similar or equal to 1/R(1-epsilon)), 0 < epsilon less than or equal to 1; we find that in any dimension the system is a non-Ferm i liquid with a quasiparticle weight which vanishes like omega epsilon /4 when omega --> 0. For ($) over cap epsilon --> 0 a marginal Fermi l iquid is obtained. A nonperturbative solution is obtained using the bo sonization method in d greater than or equal to 1 dimensions. Within t he same formalism we investigate also the electron-phonon interaction in dimensions d=3-epsilon. When the coupling constant is imaginary, on e obtains a time-dependent potential similar to what is obtained for f ermions coupled to transversed U(1) gauge bosons. A non-Fermi-liquid b ehavior is found for d less than or equal to 3.