From Classical to Quantum Fields

Quantum field theory has become the universal language of most modern theoretical physics. This book is meant to provide an introduction to this subject with particular emphasis on the physics of the fundamental interactions and elementary particles. It is addressed to advanced undergraduate, or beginning graduate, students, who have majored in physics or mathematics. The ambition is to show how these two disciplines, through their mutual interactions over the past hundred years, have enriched themselves and have both shaped our understanding of the fundamental laws of nature. The subject of this book, the transition from a classical field theory to the corresponding Quantum Field Theory through the use of Feynman’s functional integral, perfectly exemplifies this connection. It is shown how some fundamental physical principles, such as relativistic invariance, locality of the interactions, causality and positivity of the energy, form the basic elements of a modern physical theory. The standard theory of the fundamental forces is a perfect example of this connection. Based on some abstract concepts, such as group theory, gauge symmetries, and differential geometry, it provides for a detailed model whose agreement with experiment has been spectacular. The book starts with a brief description of the field theory axioms and explains the principles of gauge invariance and spontaneous symmetry breaking. It develops the techniques of perturbation theory and renormalisation with some specific examples. The last Chapters contain a presentation of the standard model and its experimental successes, as well as the attempts to go beyond with a discussion of grand unified theories and supersymmetry.