Gauge fields: introduction to quantum theory

A detailed exposition of quantum dynamics of gauge fields is presented. The classical dynamics of gauge fields and their geometric meaning are described first. Then a detailed exposition of path integral method in quantum theory is given. It is shown that this method allows consideration of all the specifics of gauge field theory. Quantization of the Yang-Mills field is discussed. Perturbation theory expansion is described in full detail, including invariant regularization and renormalization schemes. In conclusion, several applications are discussed: unified models of weak electromagnetic interactions, asymptotic freedom; gauge theories of strong interactions. 98 references, 19 figures