An Introduction To Quantum Field Theory - M. Peskin, D. Schroeder (Perseus, 1995) · Problem 12.2

The Renormalization Group — M. Peskin, D. Schroeder (Perseus, 1995)

Physics — QFT · renormalization-group-beta-functions

Problem

Beta function of the Gross-Neveu model. Compute

\beta(g)

in the two-dimensional Gross-Neveu model studied in Problem 11.3,

\mathcal{L} = \bar{\psi}_i i\partial\!\!\!/\psi_i + \frac{1}{2}g^2(\bar{\psi}_i\psi_i)^2,

with

i = 1, \ldots, N

. You should find that this model is asymptotically free. How was that fact reflected in the solution to Problem 11.3?