Gauge Field Theories

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