As a student, I was rearing at the bit, after a course on quantum mechanics, to learn quantum field theory, but the books on the subject all seemed so formidable.Fortunately, I came across a little book by Mandl on field theory, which gave me a taste of the subject enabling me to go on and tackle the more substantive texts. I have since learned that other physicists of my generation had similar good experiences with Mandl.

Preface

Convention, Notation, and Units

PART I MOTIVATION AND FOUNDATION

I.1 Who Needs It?

I.2 Path Integral Formulation of Quantum Physics

I.3 From Mattress to Field

I.4 From Field to Particle to Force

I.5 Coulomb and Newton: Repulsion and Attraction

I.6 Inverse Square Law and the Floating 3-Brane

I.7 Feynman Diagrams

I.8 Quantizing Canonically and Disturbing the Vacuum

I.9 Symmetry

I.10 Field Theory in Curved Spacetime

I.11 Field Theory Redux

PART II DIRAC AND THE SPINOR

II.1 The Dirac Equation

II.2 Quantizing the Dirac Field

II.3 Lorentz Group and Weyl Spinors

II.4 Spin-Statistics Connection

II.5 Vacuum Energy, Grassmann Integrals, and Feynman Diagrams for Fermions

II.6 Electron Scattering and Gauge Invariance

II.7 Diagrammatic Proof of Gauge Invariance

PART III RENORMALIZATION AND GAUGE INVARIANCE

III.1 Cutting Off Our Ignorance

III.2 Renormalizable versus Nonrenormalizable

III.3 Counterterms and Physical Perturbation Theory

III.4 Gauge Invariance: A Photon Can Find No Rest

III.5 Field Theory without Relativity

III.6 The Magnetic Moment of the Electron

III.7 Polarizing the Vacuum and Renormalizing the Charge

PART IV SYMMETRY AND SYMMETRY BREAKING

IV.1 Symmetry Breaking

IV.2 The Pion as a Nambu-Goldstone Boson

IV.3 Effective Potential

IV.4 Magnetic Monopole

IV.5 Nonabelian Gauge Theory

IV.6 The Anderson-Higgs Mechanism

IV.7 Chiral Anomaly

PART V FIELD THEORY AND COLLECTIVE PHENOMENA

V.1 Superfluids

V.2 Euclid, Boltzmann, Hawking, and Field Theory at Finite Temperature

V.3 Landau-Ginzburg Theory of Critical Phenomena

V.4 Superconductivity

V.5 Peierls Instability

V.6 Solitons

V.7 Vortices, Monopoles, and Instantons

PART VI FIELD THEORY AND CONDENSED MATTER

VI.1 Fractional Statistics, Chern-Simons Term, and Topological Field Theory

VI.2 Quantum Hall Fluids

VI.3 Duality

VI.4 The a Models as Effective Field Theories

VI.5 Ferromagnets and Antiferromagnets

VI.6 Surface Growth and Field Theory

VI.7 Disorder: Replicas and Grassmannian Symmetry

VI.8 Renormalization Group Flow as a Natural Concept in High Energy and Condensed Matter Physics

PART VII GRAND UNIFICATION

VII.1 Quantizing Yang-Mills Theory and Lattice Gauge Theory

VII.2 Electroweak Unification

VII.3 Quantum Chromodynamics

VII.4 Large N Expansion

VII.5 Grand Unification

VII.6 Protons Are Not Forever

VII.7 SO(10) Unification

PART VIII GRAVITY AND BEYOND

VIII.1 Gravity as a Field Theory and the Kaluza-Klein Picture

VIII.2 The Cosmological Constant Problem and the Cosmic Coincidence Problem

VIII.3 Effective Field Theory Approach to Understanding Natu.r

VIII.4 Supersymmetry: A Very Brief Introduction

VIII.5 A Glimpse of String Theory as a 2-Dimensional

Field Theory Closing Words

APPENDIXES

A Gaussian Integration and the Central Identity of Quantum Field Theory

B A Brief Review of Group Theory

C Feynman Rules

D Various Identities and Feynman Integrals

E Dotted and Undotted Indices and the Majorana Spinor

Solutions to Selected Exercises

Further Reading

Index