The main goal of this book is to familiarize the reader with a tool, the path integral, that not only offers an alternative point of view on quantum mechanics, but more importantly, under a generalized form, has also become the key to a deeper understanding of quantum field theory and its applications, extending from particle physics to phase transitions or properties of quantum gases.
Path integrals are mathematical objects that can be considered as generalizations to an infinite number of variables, represented by paths, of usual integrals. They share the algebraic properties of usual...

This work tries to provide an elementary introduction to the notions of continuum limit and universality in statistical systems with a large number of degrees of freedom. The existence of a continuum limit requires the appearance of correlations at large distance, a situation that is encountered in second order phase transitions, near the critical temperature. In this context, we will emphasize the role of gaussian distributions and their relations with the mean field approximation and Landau's theory of critical phenomena. We will show that quasi-gaussian or mean-field approximations cannot...

This work tries to provide an elementary introduction to the notions of continuum limit and universality in statistical systems with a large number of degrees of freedom. The existence of a continuum limit requires the appearance of correlations at large distance, a situation that is encountered in second order phase transitions, near the critical temperature. In this context, we will emphasize the role of gaussian distributions and their relations with the mean field approximation and Landau's theory of critical phenomena. We will show that quasi-gaussian or mean-field approximations cannot...

The International Conference on Theoretical Physics, TH-2002, took place in Paris from July 22 to 27 in the Conference Center of the UNESCO, the United Nations Educational Scientific and Cultural Organization, under aegis of the IUPAP, the International Union of Pure and Applied Physics and of the French and Euro pean Physical Societies, with a large support of several French, European and international Institutions. International and crossdisciplinary, TH-2002 welcomed around 1200 partic ipants representing all domains of modern theoretical physics. The conference offered a high-level...

The understanding of phase transitions has long been a fundamental problem of statistical mechanics. It has made spectac ular progress during the last few years, largely because of the ideas of K.G. Wilson, in applying to an apparently quite different domain the methods of the renormalization group, which had been developped in the framework of the quantum theory of fields. The ability of these theoretical methods to lead to very precise predictions has, n turn, stimulated in the last few years more refined experiments in different areas. We now have entered a period where the theoretical...