Gauge Fields: An Introduction To Quantum Theory PDF

Preface to the Second Revised (Russian) Edition

During the past ten years, since the first edition of this book, gauge invariant models of elementary particle interactions were transformed from an attractive plausible hypothesis into a generally accepted theory confirmed by experiments. It was therefore natural that the development of the methods of gauge fields attracted the attention of the great majority of specialists in quantum field theory. The new interesting lines of activity that arose in this period included the formulation of gauge theories on a lattice, the investigation of non-trivial classical solutions of the Yang-Mills equations and quantization in their neighborhood, the application of methods of algebraic topology in gauge field theory. In preparing the second edition of our book we were confronted with a difficult dilemma: either we were to extend the book significantly by including a serious discussion of the novel fields of research, or we would, in the main, adopt the same plan as for the first edition. We decided in favour of the latter version, since, in our opinion, the most promising issues mentioned above have not as yet attained a completed form. Besides, an exposition of these issues would require a significant extension of the mathematical apparatus utilized. Therefore, in the second edition we limited ourselves to presenting such supplements that are related in a natural way to the main content of the first edition, and we also introduced a number of improvements which, as we hope, should facilitate reading of the book and render it more selfconsistent.

This Preface is being written just at a time, when hopes are arising that a more fundamental basis is to be developed for elementary particle theory, the theory of superstrings.

However, independently of whether these hopes come true, gauge field theory, clearly, describes the physics of elementary particles adequately at moderate energies. Besides, the methods applied in the field theory of relativistic strings represent a direct generalization of the methods of gauge field theory, to which this book is devoted. For this reason we consider a new edition of it to be useful, both for direct applications of the already developed gauge theory and for search of new ways.

Author: L. D. Faddeev