Gauge theory is now recognized as one of the most revolutionary discoveries in physics since the development of quantum mechanics. This primer explains how and why gauge theory has dramatically changed our view of the fundamental forces of nature. The text is designed for the non-specialist. A new, intuitive approach is used to make the ideas of gauge theory accessible to both scientists and students with only a background in quantum mechanics. Emphasis is placed on the physics rather than the formalism.
This text provides a framework for describing and organizing the basic forces of nature and the interactions of subatomic particles. A detailed and self-contained mathematical account of gauge theory, it is geared toward beginning graduate students and advanced undergraduates in mathematics and physics. This well-organized treatment supplements its rigor with intuitive ideas. Starting with an examination of principal fiber bundles and connections, the text explores curvature; particle fields, Lagrangians, and gauge invariance; Lagrange's equation for particle fields; and the inhomogeneous field equation. Additional topics include free Dirac electron fields; interactions; calculus on frame bundle; and unification of gauge fields and gravitation. The text concludes with references, a selected bibliography, an index of notation, and a general index.
Gauge theory, which underlies modern particle physics as well as the theory of gravity, and hence all of physics as we know it today, is itself based on a few fundamental concepts, the consequences of which are often as beautiful as they are deep. Unfortunately, in view of the pressure to cover aspects of the theory that are necessary for its many important applications, very little space is usually devoted in textbooks and graduate courses to the treatment of these concepts. The present small volume is an attempt to help in some degree to redress this imbalance in the literature.The topics covered are elementary in the sense of being basic, not in the sense of being shallow or easy. Although all will already feature at the classical field level, and most even before the introduction of an action principle, they often lead one to pose some quite profound questions, so that much of the material treated is by necessity at the front line of research. The approach adopted is physically motivated, although there is no hesitation in introducing mathematical concepts when they are a help to understanding. In the presentation, little is assumed of the reader, and no pains has been spared to make the whole volume understandable to researchers in other fields and to graduate students, provided that the reader is willing to devote sufficient effort required by the subject matter. On the other hand, neither has there been any conscious attempt to avoid essential difficulties, or to trivialise concepts which are intrinsically abstruse. It is thus hoped that the result will be enjoyable reading for researchers and students alike.
Written by world-leading experts in particle physics, this new book from Luciano Maiani and Omar Benhar, with contributions from the late Nicola Cabibbo, is based on Feynman’s path integrals. Key elements of gauge theories are described—Feynman diagrams, gauge-fixing, Faddeev-Popov ghosts—as well as renormalization in Quantum Electrodynamics. Quarks and QCD interactions are introduced. Renormalization group and high momentum behaviour of the coupling constants is discussed in QED and QCD, with asymptotic freedom derived at one-loop. These concepts are related to the Higgs boson and models of grand unification. "... an excellent introduction to the quantum theory of gauge fields and their applications to particle physics. ... It will be an excellent book for the serious student and a good reference for the professional practitioner. Let me add that, scattered through the pages, we can find occasional traces of Nicola Cabibbo's style." —John Iliopoulos, CNRS-Ecole Normale Supérieure " ... The volume ends with an illuminating description of the expectation generated by the recent discovery of the Higgs boson, combined with the lack of evidence for super-symmetric particles in the mass range 0.6-1 TeV." —Arturo Menchaca-Rocha, FinstP, Professor of Physics, Mexico’s National Autonomous University, Former President of the Mexican Academy of Sciences, Presidential Advisor "...The reader is masterfully guided through the subtleties of the quantum field theory and elementary particle physics from simple examples in Quantum Mechanics to salient details of modern theory." —Mikhail Voloshin, Professor of Physics, University of Minnesota
This book presents in a unified way modern geometric methods in analytical mechanics based on the application of fibre bundles, jet manifold formalism and the related concept of connection. Non-relativistic mechanics is seen as a particular field theory over a one-dimensional base. In fact, the concept of connection is the major link throughout the book. In the gauge scheme of mechanics, connections appear as reference frames, dynamic equations, and in Lagrangian and Hamiltonian formalisms. Non-inertial forces, energy conservation laws and other phenomena related to reference frames are analyzed; that leads us to observable physics. The gauge formulation of classical mechanics is extended to quantum mechanics under different reference frames. Special topics on geometric BRST mechanics, relativistic mechanics and others, together with many examples, are also dealt with.
Presents recent advances of perturbative relativistic field theory in a pedagogical and straightforward way. For graduate students who intend to specialize in high-energy physics.
Emphasis is placed on analogies between the various systems rather than on advanced or specialized aspects, with the purpose of illustrating common ideas within different domains of physics. Starting from a basic knowledge of quantum mechanics and classical electromagnetism, the exposition is self-contained and explicitly details all steps of the derivations. The new edition features a substantially new treatment of nucleon pairing.
This volume is a compilation of works which, taken together, give a complete and consistent presentation of instanton calculus in non-Abelian gauge theories, as it exists now. Some of the papers reproduced are instanton classics. Among other things, they show from a historical perspective how the instanton solution has been found, the motivation behind it and how the physical meaning of instantons has been revealed. Other papers are devoted to different aspects of instanton formalism including instantons in supersymmetric gauge theories. A few unsolved problems associated with instantons are described in great detail. The papers are organized into several sections that are linked both logically and historically, accompanied by extensive comments.
Mathematical physics has made enormous strides over the past few decades, with the emergence of many new disciplines and with revolutionary advances in old disciplines. One of the especially interesting features is the link between developments in mathematical physics and in pure mathematics. Many of the exciting advances in mathematics owe their origin to mathematical physics — superstring theory, for example, has led to remarkable progress in geometry — while very pure mathematics, such as number theory, has found unexpected applications.The beginning of a new millennium is an appropriate time to survey the present state of the field and look forward to likely advances in the future. In this book, leading experts give personal views on their subjects and on the wider field of mathematical physics. The topics covered range widely over the whole field, from quantum field theory to turbulence, from the classical three-body problem to non-equilibrium statistical mechanics.
This monograph aims to provide a unified, geometrical foundation of gauge theories of elementary particle physics. The underlying geometrical structure is unfolded in a coordinate-free manner via the modern mathematical notions of fibre bundles and exterior forms. Topics such as the dynamics of Yang-Mills theories, instanton solutions and topological invariants are included. By transferring these concepts to local space-time symmetries, generalizations of Einstein's theory of gravity arise in a Riemann-Cartan space with curvature and torsion. It provides the framework in which the (broken) Poincaré gauge theory, the Rainich geometrization of the Einstein-Maxwell system, and higher-dimensional, non-abelian Kaluza-Klein theories are developed. Since the discovery of the Higgs boson, concepts of spontaneous symmetry breaking in gravity have come again into focus, and, in this revised edition, these will be exposed in geometric terms. Quantizing gravity remains an open issue: formulating it as a de Sitter type gauge theory in the spirit of Yang-Mills, some new progress in its topological form is presented. After symmetry breaking, Einstein’s standard general relativity with cosmological constant emerges as a classical background. The geometrical structure of BRST quantization with non-propagating topological ghosts is developed in some detail.
