Dedication

pp v-vi

Contents

pp vii-xvi

Preface

pp xvii-xvii

Acknowledgements

pp xviii-xviii

Introduction

pp xix-xx

Part I - General Properties of Fields; Scalars and Gauge Fields

pp 1-2

1 - Short Review of Classical Mechanics

pp 3-13

2 - Symmetries, Groups, and Lie algebras; Representations

pp 14-23

3 - Examples: The Rotation Group and SU(2)

pp 24-35

4 - Review of Special Relativity: Lorentz Tensors

pp 36-45

5 - Lagrangeans and the Notion of Field; Electromagnetism as a Field Theory

pp 46-53

6 - Scalar Field Theory, Origins, and Applications

pp 54-64

7 - Nonrelativistic Examples:WaterWaves and Surface Growth

pp 65-73

8 - Classical Integrability: Continuum Limit of Discrete, Lattice, and Spin Systems

pp 74-80

9 - Poisson Brackets for Field Theory and Equations of Motion: Applications

pp 81-88

10 - Classical Perturbation Theory and Formal Solutions to the Equations of Motion

pp 89-96

11 - Representations of the Lorentz Group

pp 97-107

12 - Statistics, Symmetry, and the Spin-Statistics Theorem

pp 108-117

13 - Electromagnetism and the Maxwell Equation; Abelian Vector Fields; Proca Field

pp 118-126

14 - The Energy-Momentum Tensor

pp 127-136

15 - Motion of Charged Particles and ElectromagneticWaves; Maxwell Duality

pp 137-149

16 - The Hopfion Solution and the Hopf Map

pp 150-157

17 - Complex Scalar Field and Electric Current: Gauging a Global Symmetry

pp 158-164

18 - The Noether Theoremand Applications

pp 165-171

19 - Nonrelativistic and Relativistic Fluid Dynamics: Fluid Vortices and Knots

pp 172-182

Part II - Solitons and Topology; Non-Abelian Theory

pp 183-184

20 - Kink Solutions in ϕ4 and Sine-Gordon, Domain Walls and Topology

pp 185-194

21 - The Skyrmion Scalar Field Solution and Topology

pp 195-202

22 - Field Theory Solitons for Condensed Matter: The XY and Rotor Model, Spins, Superconductivity, and the KT Transition

pp 203-208