Communications in Mathematical Physics, 160, 93--172, 1994
G. Benfatto, G. Gallavotti, A. Procacci, B. Scoppola
Beta function and Schwinger functions for a many fermions
system in one dimension. Anomaly of the Fermi surface.
Abstract:
We present a rigorous discussion of the analyticity
properties of the beta function and of the effective potential for the
theory of the ground state of a one dimensional system of many spinless
fermions. We show that their analyticity domain as a function of the
running couplings is a polydisk with positive radius bounded below,
uniformly in all the cut offs (infrared and ultraviolet) necessary to
give a meaning to the formal Schwinger functions. We also prove the
vanishing of the scale independent part of the beta function showing
that this implies the analyticity of the effective potential and of the
Schwinger functions in terms of the bare coupling. Finally we show that
the pair Schwinger function has an anomalous long distance behaviour.