QUANTUM FIELDS AT FINITE TEMPERATURE: A BRIEF INTRODUCTION

摘要

These lectures are a brief introduction to the methods of 'finite temperature field theory". By this one refers to a collection of technique s which have been developed, for a large part of them, long ago in the context of quantum statistical mechanics, the so-called "many-body" problem. These were typically applied to non relativistic systems such as the electron gas, liquid Helium, nuclear matter, etc. More recently, these methods have been extended to systems of relativistic particles interacting with gauge fields, for which new interesting technical and conceptual issues appear. The interest for such questions was originally triggered by the developments which took place in particle physics in the early seventies, when it was understood that elementary particle interactions could be unified in he framework of gauge theories. Two essential concepts emerged then: spontaneous symmetry breaking providing a mechanism for the generation of particle nasses, and asymptotic freedom according to which the interactions become wea c at short distances. These developments changed our ideas about matter at Ugh temperature or density. Because thermal fluctuations tend to suppress the expectation value of the fields responsible for symmetry breaking giving masssas to the particles, one expects all particles to become massless at high temperature. Furthermore, because of asymptotic freedom, theses massless particles nteract weakly. Thus at high enough temperature, matter becomes simple and turns essentially into an ultrelativistic plasma of weakly interacting particles.