Gauge Fields

An Introduction To Quantum Theory, Second Edition

L. D. Faddeev

• Publisher: CRC Press
• Year: 2018
• ISBN:
  9780429973451
• Edition: 2
• Topic: Physical Sciences
• Subtopic: Physics
• Index: Physics

Gauge field theory 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 the author considers a new edition of it to be useful, both for direct applications of the already developed gauge theory and for search of new ways.

1

Introduction:
Fundamentals of Classical Gauge Field Theory

1.1 Basic Concepts and Notation

The theory of gauge fields at present represents the widely accepted theoretical basis of elementary particle physics. Indeed, the most elaborate model of field theory, quantum electrodynamics, is a particular case of the gauge theory. Further, models of weak interactions have acquired an elegant and self-consistent formulation in the framework of gauge theories. The phenomenological four-fermion interaction has been replaced by the interaction with an intermediate vector particle, the quantum of the Yang-Mills field. Existing experimental data along with the requirement of gauge invariance led to the prediction of weak neutral currents and of new quantum numbers for hadrons.

Phenomenological quark models of strong interactions also have their most natural foundation in the framwork of a gauge theory known as quantum chromodynamics. This theory provides a unique possibility of describing, in the framework of quantum field theory, the phenomenon of asymptotic freedom. This theory also affords hopes of explaining quark confinement, although this question is not quite clear.

Finally, the extension of the gauge principle may lead to the gravitational interaction also being placed in the general scheme of Yang-Mills fields.

So the possibility arises of explaining, on the basis of one principle, all the hierarchy of interactions existing in nature. The term unified field theory, discredited sometime ago, now acquires a new reality in the framework of gauge field theories. In the formation of this picture a number of scientists took part. Let us mention some of the key dates.

In 1953 C. N. Yang and R. L. Mills, for the first time, generalized the principle of gauge invariance of the interaction of electric charges to the case of interacting isospins....

Table of contents

• Cover
• Title Page
• Half Title
• Copyright Page
• Table of Contents
• Preface to the Second Revised (Russian) Edition
• Preface to the Original (Russian) Edition
• 1 Introduction: Fundamentals of Classical Gauge Field Theory
• 2 Quantum Theory in Terms of Path Integrals
• 3 Quantization of the Yang-Mills Field
• 4 Renormalization of Gauge Theories
• 5 Some Applications and Conclusion
• Bibliography Notes
• Supplement in Proof: Anomalous Commutator of The Gauss Law
• References
• Notation