# Gauge Field Theories

### An Introduction

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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

Problems

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

Problems

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

Problems

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

Problems

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

Problems

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

Problems

Chapter VII: The Higgs mechanism

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

VII.2 - Goldstone bosons

VII.3 - The Higgs mechanism

Problems

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

Problems

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

Problems

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

Problems

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

References

Index

## Product details

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