Quantum field theory has remained throughout the years one of the most important tools in understanding the microscopic world. The recent years have seen a blossoming of developments and applications which go far beyond the original scope.
Our attempt at presenting a pedagogical survey of this subject arose from lectures given in Orsay and Saclay, and first materialized in a set of notes written in French. As with any such endeavor it reflects to a large extent our prejudices and enthusiasms, even though we have tried to be as thorough as possible and to keep a balance between the formalism and practical examples of calculations. In its present version this book addresses itself both to students and researchers in field theory, particle physics, and related areas. It presupposes a general background in quantum mechanics, electrodynamics, and relativity, and assumes some familiarity with classical calculus including group theory and complex analysis.
To avoid one-sided views, we have respected the historical perspective and given equal weight to the operator formulation, propagator approach, and more synthetic path integral representation. Nevertheless, this is by no means a complete treatise. We list some of the main omissions. For lack of space and because we felt incompetent we do not treat axiomatic field theory and critical phenomena in statistical mechanics. Specific topics such as a detailed study of the Poincare group and its representations, higher spin fields, a thorough discussion of infrared problems, gravitational interactions, two-dimensional models, etc., could not be discussed here.