1990


Renormalization group

These are the lecture notes of a course given at the IIIe cycle de la Suisse Romande, in january/february 1990,
at the Universite' de Lausanne
(Institut de Physique The'orique).



Contents

1 Introduction
2 Problems equivalent to the analysis of suitable functional integrals
3 Other functional integrals
4 Effective potentials and Schwinger functions
5 Multiscale decomposition of propagators and fields. Running effective potentials
6 Renormalization group. Relevant and irrelevant components of the effective potentials
7 Asymptotic freedom. Upper critical dimension
8 Beyond the linear approximation. The beta function and perturbation theory
9 The beta function as a dynamical system. Asymptotic freedom of marginal theories
10 Anomalous dimension
11 The Fermi liquid and the Luttinger model
12 The generic critical point for d=3, gamma=0 and the epsilon-expansion
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Troisie`me cycle de la physique en Suisse Romande
Service des publications
Universite' de Lausanne
BSP, Dorigny
CH-1015 Lausanne
Switzerland