Gauge Field Theories

Gauge Field Theories

An Introduction

1st Edition - January 1, 1981

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  • Author: J. Leite Lopes
  • eBook ISBN: 9781483278971

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Gauge Field Theories: An Introduction covers the basic notions and principles of gauge theories. This book is composed of 10 chapters that focus on the Salam-Weinberg model of electro-weak interactions of neutrino-lepton scattering, as well as the Parton model. The first chapter is an introduction to solitons and instantons, as well as the topological quantum numbers, subjects that arose from the study of the non-linear field equations in gauge theories. The succeeding chapters deal with the concept of gravitational field, electrodynamical systems, the Yang-mills gauge fields, and the Higgs mechanism. The remaining chapters highlight the speculations on possible lepton and quark structured. These chapters present the SU(5) model of grand unification. This book will prove useful to physics university and advanced high school students.

Table of Contents

  • Introduction

    Table I - Basic interactions

    Table II - Observed fermions

    Table III - Observed bosons

    Table IV - Quark quantum numbers

    Table V - Lepton quantum numbers

    Table VI - Basic fermions

    Table VII - Basic boson fields

    Table VIII - Quark structure of hadrons

    Table IX - Questions

    Chapter I : Field equations, conserved tensors and topological quantum numbers

    I.1 - Free field equations

    I.2 - Non-linear field equations for a single scalar field

    I.3 - Non-linear vector field equations

    I.4 - Field equations and action principle

    I.5 - Examples of lagrangeans

    I.6 - Noether's conserved tensors

    I.7 - Examples of Noether tensors

    I.8 - Conserved Noether tensors for specific fields

    I.9 - Soliton solutions of classical non-linear field equations and topological quantum numbers


    Chapter II: The electromagnetic gauge field

    II.1 - Field interactions

    II.2 - The electromagnetic field as a gauge field

    II.3 - Maxwell's equations and the photon propagator ; gauge fixing conditions

    II.4 - The energy momentum tensor of fields in interaction with the electromagnetic field

    II.5 - Non-integrable phase factor and the integral formulation of gauge field theories


    Chapter III: Examples of electrodynamical systems

    III.1 - Scalar electrodynamics

    III.2 - Proca vector field electrodynamics

    III.3 - Spinor field electrodynamics

    III.4 - Scalar and Proca electrodynamics: alternative formulations


    Chapter IV : The Yang-Mills gauge field

    IV.1 - The isospin current

    IV.2 - The Yang-Mills isospin gauge-field

    IV.3 - The isospin gauge field as a mixture of an abelian gauge field and an isovector

    IV.4 - Lagrangean of a Yang-Mills isospin gauge field in interaction with matter

    IV.5 - Field equations and non-linearity of the interaction

    IV.6 - Remarks on the covariant derivative

    IV.7 - Energy momentum tensor for a Yang-Mills system

    IV.8 - Examples of 7ang-MiHs isospin gauge systems of fields

    IV.9 - The global SU(3) group

    IV.10 - The colour gauge field


    Chapter V.: The gravitational gauge field

    V.1 - Introduction

    V.2 - Groups of local transformations and covariant derivatives

    V.3 - Covariant derivatives of tensors in general relativity: the gravitational gauge field

    V.4 - The lagrangean of matter tensor fields in interaction with the gravitational field

    V.5 - Einstein's equation of the gravitational field

    V.6 - The energy momentum of the gravitational field

    V.7 - Gravitational interaction with an electromagnetic field

    V.8 - The tetrad formalism

    V.9 - Dirac's equation and current in general relativity

    V.10 - The Dirac Field energy-momentum tensor

    V.11 - Gauge fixing conditions


    Chapter VI.: Weak interactions and intermediate vector bosons

    VI.1 - Introduction

    VI.2 - Charged weak currents

    VI.3 - The intermediate vector boson field

    VI.4 - High-energy divergences in the Fermi and vector boson theories


    Chapter VII: The Higgs mechanism

    VII.1 - The notion of spontaneous symmetry break-down

    VII.2 - Goldstone bosons

    VII.3 - The Higgs mechanism


    Chapter VIII: The Salam-Weinberg model

    VIII. 1 - Unification of the electromagnetic and weak interaction theories: The Salam-Weinberg model

    VIII.2 - The SU(2) U(l) gauge in variant lagrangean

    VIII.3 - Generation of the electron mass

    VIII.4 - The mass of the physical Higgs field

    VIII.5 - The massive vector bosons

    VIII.6 - The electromagnetic field and the Weinberg angle

    VIII.7 - The effective Salam-Weinberg lagrangean for electrons and neutrinos

    VIII.8 - Parameters and physical constants in the Salam-Weinberg lepton model

    VIII.9 - The neutral lepton currents

    VIII.10 - Extension of the model to the other leptons

    VIII.11 - Neutrino-lepton scattering and the experimental tests of the Salam-Weinberg model

    VIII.12 - The Salam-Weinberg model for hadrons ; the GIM mechanism ; the quark masses

    VIII.13 - The Salam-Weinberg quark currents

    VIII.14 - The suppression of the strangeness-changing neutral current

    VIII.15 - Estimates of the quark masses

    VIII.16 - The parton-quark model

    VIII.17 - The value of the Weinberg angle for the neutrinonucleon scattering


    Chapter IX: Gauge theory with lepton flavour non-conservation

    IX.1 - SU(2) U(l) gauge theory with heavy leptons

    IX.2 - Speculations on lepton structure 331


    Chapter X: Attempts at a "grand" unification: the SU(5) model

    X.1 - The SU(5) gauge fields and generators

    X.2 - Hierarchy of spontaneous broken symmetries; Lepto-quark bosons

    X.3 - Concluding remarks


    Solutions of Problems

    Reprinted Nobel lectures:

    Conceptual foundations of the unified theory of weak and electromagnetic interactions. Les Prix Nobel 1979

    Gauge unification of fundamental forces. Les Prix Nobel 1979

    Towards a unified theory: threads in a tapestry. Les Prix Nobel 1979



Product details

  • No. of pages: 500
  • Language: English
  • Copyright: © Pergamon 2013
  • Published: January 1, 1981
  • Imprint: Pergamon
  • eBook ISBN: 9781483278971

About the Author

J. Leite Lopes

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