From Classical to Quantum Fields

This book is an introduction to the modern ways of teaching classical and quantum field theories. A key tool is symmetries. For the resolution of classical theories, special attention is given to the definition of advanced or retarded potentials to ease the understanding of path integrals. The Path integral is used as the conceptual tool for defining the quantum field theories. The classical formalism is presented as a useful way to concretely compute observables that one defines in the path integral framework. The book contains special chapters which are devoted to new domains which have not been presented in other texts. They include constructive quantum field theories and topological field theory.