Note: Cover -- Half-title -- Series-title -- Title -- Copyright -- Contents -- Preface -- 1 Introduction -- 1.1 Solitons as particles -- 1.2 A brief history of topological solitons -- 1.3 Bogomolny equations and moduli spaces -- 1.4 Soliton dynamics -- 1.5 Solitons and integrable systems -- 1.6 Solitons - experimental status -- 1.7 Outline of this book -- 2 Lagrangians and fields -- 2.1 Finite-dimensional systems -- 2.2 Symmetries and conservation laws -- 2.3 Field theory -- 2.4 Noether's theorem in field theory -- 2.5 Vacua and spontaneous symmetry breaking -- 2.6 Gauge theory -- 2.7 The Higgs mechanism -- 2.8 Gradient flow in field theory -- 3 Topology in field theory -- 3.1 Homotopy theory -- 3.2 Topological degree -- 3.3 Gauge fields as differential forms -- 3.4 Chern numbers of abelian gauge .elds -- 3.5 Chern numbers for non-abelian gauge fields -- 3.6 Chern-Simons forms -- 4 Solitons - general theory -- 4.1 Topology and solitons -- 4.2 Scaling arguments -- 4.3 Symmetry and reduction of dimension -- 4.4 Principle of symmetric criticality -- 4.5 Moduli spaces and soliton dynamics -- 5 Kinks -- 5.1 Bogomolny bounds and vacuum structure -- 5.2 Phi4 kinks -- 5.3 Sine-Gordon kinks -- 5.4 Generalizations -- 6 Lumps and rational maps -- 6.1 Lumps in the O(3) sigma model -- 6.2 Lumps on a sphere and symmetric maps -- 6.3 Stabilizing the lump -- 7 Vortices -- 7.1 Ginzburg-Landau energy functions -- 7.2 Topology in the global theory -- 7.3 Topology in the gauged theory -- 7.4 Vortex solutions -- 7.5 Forces between gauged vortices -- 7.6 Forces between vortices at large separation -- 7.7 Dynamics of gauged vortices -- 7.7.1 Second order dynamics -- 7.7.2 Gradient flow -- 7.7.3 First order dynamics -- 7.8 Vortices at critical coupling -- 7.9 Moduli space dynamics -- 7.10 The metric on MN -- 7.11 Two-vortex scattering. , 7.12 First order dynamics near critical coupling -- 7.13 Global vortex dynamics -- 7.14 Varying the geometry -- 7.14.1 Volume of moduli space -- 7.14.2 Toroidal geometry - the Abrikosov lattice -- 7.14.3 Vortices on the hyperbolic plane -- 7.15 Statistical mechanics of vortices -- 8 Monopoles -- 8.1 Dirac monopoles -- 8.2 Monopoles as solitons -- 8.3 Bogomolny-Prasad-Sommerfield monopoles -- 8.4 Dyons -- 8.5 The Nahm transform -- 8.6 Construction of monopoles from Nahm data -- 8.7 Spectral curves -- 8.8 Rational maps and monopoles -- 8.9 Alternative monopole methods -- 8.10 Monopole dynamics -- 8.11 Moduli spaces and geodesic motion -- 8.12 Well separated monopoles -- 8.13 SU(m) monopoles -- 8.14 Hyperbolic monopoles -- 9 Skyrmions -- 9.1 The Skyrme model -- 9.2 Hedgehogs -- 9.3 Asymptotic interactions -- 9.4 Low charge Skyrmions -- 9.5 The rational map ansatz -- 9.6 Higher charge Skyrmions -- 9.7 Lattices, crystals and shells -- 9.8 Skyrmion dynamics -- 9.9 Generalizations of the Skyrme model -- 9.10 Quantization of Skyrmions -- 9.11 The Skyrme-Faddeev model -- 10 Instantons -- 10.1 Self-dual Yang-Mills fields -- 10.2 The ADHM construction -- 10.3 Symmetric instantons -- 10.4 Skyrme fields from instantons -- 10.5 Monopoles as self-dual gauge fields -- 10.6 Higher rank gauge groups -- 11 Saddle points - sphalerons -- 11.1 Mountain passes -- 11.2 Sphalerons on a circle -- 11.3 The gauged kink -- 11.4 Monopole-antimonopole dipole -- 11.5 The electroweak sphaleron -- 11.6 Unstable solutions in other theories -- References -- Index.

Note: Cover -- Preface -- Contents -- 0 Introduction -- 1 Fundamental Ideas -- 1.1 Variational Principles -- 1.1.1 Geometrical optics-reflection and refraction -- 1.1.2 The scope of variational principles -- 1.2 Euclidean Space and Time -- 1.3 Partial Derivatives -- 1.4 e, π and Gaussian Integrals -- 1.4.1 Radioactive decay -- 1.4.2 Waves and periodic functions -- 1.4.3 The Gaussian integral -- 1.4.4 The method of steepest descents -- 2 Motions of Bodies-Newton's Laws -- 2.1 Introduction -- 2.2 Newton's Laws of Motion -- 2.3 The Principle of Least Action -- 2.3.1 Motion in one dimension -- 2.3.2 A simple example and a simple method -- 2.3.3 Motion in a general potential and Newton's second law -- 2.3.4 The calculus of variations -- 2.3.5 The unimportance of the endpoints -- 2.4 The Motion of Several Bodies and Newton's Third Law -- 2.5 Motion of One Body in Three Dimensions -- 2.5.1 The harmonic oscillator -- 2.6 Central Forces -- 2.6.1 Circular orbits -- 2.7 The Attractive Inverse Square Law Force -- 2.8 G and the Mass of the Earth -- 2.9 Composite Bodies and Centre of Mass Motion -- 2.10 The Kepler 2-Body Problem -- 2.10.1 Binary stars -- 2.11 Lagrangian Points -- 2.12 Conservation of Energy -- 2.13 Friction and Dissipation -- 3 Fields-Maxwell's Equations -- 3.1 Fields -- 3.2 The Scalar Field Equation -- 3.3 Waves -- 3.4 Divergence and Curl -- 3.5 Electromagnetic Fields and Maxwell's Equations -- 3.5.1 What Maxwell's equations tell us -- 3.6 Electrostatic Fields -- 3.6.1 Charge and dipole moment -- 3.7 Electromagnetic Waves -- 3.8 Magnetostatics -- 3.9 Principle of Least Action for Electromagnetic Fields -- 3.10 The Lorentz Force -- 3.10.1 The Lorentz force from the principle of least action -- 3.11 Field Energy and Momentum -- 3.12 Dynamics of Particles and Fields -- 4 Special Relativity -- 4.1 Introduction -- 4.2 Lorentz Transformations. , 4.3 Relativistic Dynamics -- 4.3.1 Comparison of Newtonian and relativistic dynamics -- 4.3.2 E = mc2 -- 4.4 More on 4-Vectors -- 4.5 The Relativistic Character of Maxwell's Equations -- 4.6 Relativistic Principles of Least Action -- 5 Curved Space -- 5.1 Spherical Geometry -- 5.1.1 Geodesics -- 5.2 Non-Euclidean, Hyperbolic Geometry -- 5.3 Gaussian Curvature -- 5.4 Riemannian Geometry -- 5.4.1 Simple examples of metrics -- 5.5 Tensors -- 5.5.1 Covariant derivatives and Christoffel symbols -- 5.5.2 Christoffel symbols in plane polar coordinates -- 5.6 The Riemann Curvature Tensor -- 5.6.1 Riemann curvature in plane polar coordinates -- 5.6.2 Riemann curvature on a sphere -- 5.6.3 The 3-sphere -- 5.7 The Geodesic Equation -- 5.7.1 Geodesics in plane polar coordinates -- 5.7.2 The equation of geodesic deviation -- 5.8 Applications -- 6 General Relativity -- 6.1 The Equivalence Principle -- 6.2 The Newtonian Gravitational Field and Tidal Forces -- 6.3 Minkowski Space -- 6.4 Curved Spacetime Geometry -- 6.4.1 Weak gravitational fields -- 6.5 The Gravitational Field Equation -- 6.5.1 The energy-momentum tensor -- 6.5.2 The Einstein tensor and the Einstein equation -- 6.5.3 Determining the constant of proportionality -- 6.6 The Classic Tests of General Relativity -- 6.6.1 The perihelion advance of Mercury -- 6.6.2 The deflection of starlight -- 6.6.3 Clocks and gravitational redshift -- 6.7 The Schwarzschild Solution of the Einstein Equation -- 6.7.1 The Newtonian limit -- 6.8 Particle Motion in Schwarzschild Spacetime -- 6.9 Light Deflection in Schwarzschild Spacetime -- 6.10 The Interior Schwarzschild Solution -- 6.11 Black Holes -- 6.11.1 Eddington-Finkelstein coordinates -- 6.11.2 The Kerr metric -- 6.12 Gravitational Waves -- 6.12.1 The detection of gravitational waves -- 6.13 The Einstein-Hilbert Action -- 7 Quantum Mechanics -- 7.1 Introduction. , 7.2 Position and Momentum in Quantum Mechanics -- 7.3 The Schrödinger Equation -- 7.3.1 The free particle -- 7.3.2 The harmonic oscillator -- 7.4 Interpretation of Wavefunctions-Observables -- 7.4.1 Position probabilities -- 7.4.2 Other physical quantities-hermitian operators -- 7.4.3 Measurements of observables -- 7.5 Expectation Values -- 7.6 After a Measurement -- 7.7 Uncertainty Relations -- 7.8 Scattering and Tunnelling -- 7.9 Variational Principles in Quantum Mechanics -- 8 Quantum Mechanics in Three Dimensions -- 8.1 Introduction -- 8.2 Position and Momentum Operators -- 8.2.1 Particle in a box -- 8.3 Angular Momentum Operators -- 8.3.1 Eigenfunctions of l2 using Cartesian coordinates -- 8.4 The Schrödinger Equation with a Spherical Potential -- 8.4.1 The Coulomb potential -- 8.4.2 Spectroscopy -- 8.5 Spin -- 8.5.1 The Stern-Gerlach experiment -- 8.5.2 The Zeeman effect -- 8.5.3 Other spin representations -- 8.6 Spin 1/2 as a Quantum Paradigm -- 8.7 Quantum Mechanics of Several Identical Particles -- 8.7.1 The Fermi sphere -- 8.8 Bosons, Fermions and Spin -- 8.9 Return to the Action -- 9 Atoms, Molecules and Solids -- 9.1 Atoms -- 9.1.1 Atomic orbitals -- 9.1.2 Atomic shell model -- 9.2 Molecules -- 9.2.1 Covalent bonding -- 9.2.2 Polar bonds -- 9.2.3 Simple molecules -- 9.3 Organic Chemistry -- 9.3.1 Hückel theory-benzene -- 9.3.2 Polyenes -- 9.4 Solids -- 9.4.1 Covalent solids -- 9.5 Band Theory -- 9.5.1 Atomic lattices -- 9.5.2 Bloch's theorem -- 9.5.3 Bloch states in a finite crystal -- 9.5.4 The tight-binding model -- 9.5.5 The nearly free electron model -- 9.5.6 Ionic solids -- 9.5.7 Example of caesium chloride -- 9.5.8 Metals -- 9.5.9 Example of copper -- 9.6 Ferromagnetism -- 10 Thermodynamics -- 10.1 Introduction -- 10.1.1 What is heat? -- 10.1.2 The ideal gas law -- 10.1.3 The microscopic origin of heat -- 10.1.4 Iced tea. , 10.2 Entropy and Temperature -- 10.3 The First Law of Thermodynamics -- 10.3.1 New variables -- 10.4 Subsystems-The Gibbs Distribution -- 10.5 The Maxwell Velocity Distribution -- 10.6 Ideal Gases-Equation of State and Entropy -- 10.7 Non-Ideal Gases -- 10.8 The Chemical Potential -- 10.9 Fermion and Boson Gases at Low Temperature -- 10.9.1 The Fermi-Dirac function -- 10.9.2 Pressure of a degenerate electron gas -- 10.9.3 The heat capacity of an electron gas -- 10.9.4 The Bose-Einstein function -- 10.10 Black Body Radiation -- 10.11 Lasers -- 10.12 Magnetization in Spin Systems -- 10.13 A Little about Phase Transitions -- 10.14 Hawking Radiation -- 11 Nuclear Physics -- 11.1 The Birth of Nuclear Physics -- 11.2 The Strong Force -- 11.2.1 The nuclear potential -- 11.2.2 Nucleon pairing -- 11.2.3 The liquid drop model -- 11.3 The Nuclear Shell Model -- 11.3.1 The atomic shell analogy -- 11.3.2 The harmonic oscillator -- 11.3.3 Spin-orbit coupling -- 11.3.4 Beta decay -- 11.3.5 The Nilsson model -- 11.4 Alpha Decay -- 11.5 Fission -- 11.6 Fusion -- 11.6.1 Thermonuclear fusion -- 11.6.2 Controlled nuclear fusion -- 11.7 The Island of Stability -- 11.8 Exotic Nuclei -- 11.9 Pions, Yukawa Theory and QCD -- 12 Particle Physics -- 12.1 The Standard Model -- 12.1.1 Fundamental particles -- 12.2 Quantum Field Theory -- 12.2.1 Quantizing the electromagnetic field -- 12.2.2 The quantized scalar Klein-Gordon field -- 12.3 The Dirac Field -- 12.3.1 The Dirac equation -- 12.3.2 Quantizing the Dirac field-particles and antiparticles -- 12.4 Actions and Interactions -- 12.4.1 Quantum electrodynamics -- 12.4.2 Feynman diagrams -- 12.5 The Strong Force -- 12.5.1 Quarks -- 12.5.2 Confinement -- 12.6 QCD -- 12.6.1 Gluons -- 12.6.2 Lattice QCD -- 12.6.3 Heavy quarks and exotic hadrons -- 12.7 The Weak Force -- 12.7.1 Parity violation. , 12.8 The Theory of the Electroweak Force -- 12.8.1 The Higgs mechanism -- 12.8.2 Fermion masses -- 12.8.3 Discovering the W and Z bosons and the Higgs boson -- 12.8.4 Quark mixing -- 12.8.5 How many generations? -- 12.9 Neutrino Oscillations -- 13 Stars -- 13.1 The Sun -- 13.2 The Herzsprung-Russell Diagram -- 13.3 The Birth of Stars -- 13.3.1 Stellar composition -- 13.3.2 The virial theorem -- 13.3.3 Star formation -- 13.4 Stellar Structure -- 13.4.1 The structure functions -- 13.4.2 The mass-luminosity relationship -- 13.4.3 The density-temperature relationship -- 13.5 Nucleosynthesis -- 13.5.1 The proton-proton chain -- 13.5.2 The CNO cycle -- 13.5.3 The mass-radius relationship -- 13.5.4 The mass-temperature relationship -- 13.5.5 Minimum mass of main sequence stars -- 13.5.6 The temperature-luminosity relationship -- 13.6 Giant Stars Beyond the Main Sequence -- 13.6.1 The triple alpha process -- 13.7 Late Evolution -- 13.7.1 White dwarfs -- 13.7.2 Gravitational collapse of massive stars -- 13.8 Neutron Stars -- 13.8.1 Pulsars -- 13.9 Supernovae -- 13.9.1 Gamma-ray bursts -- 13.10 The Density-Temperature Diagram -- 14 Cosmology -- 14.1 Einstein's Universe -- 14.2 The Distance-Redshift Relationship -- 14.3 Friedmann-Robertson-Walker Cosmology -- 14.3.1 Einstein's equation and the FRW metric -- 14.3.2 The general FRW cosmological solutions -- 14.4 Cosmological Redshift -- 14.5 Newtonian Interpretation of the FRW Cosmology -- 14.6 The Big Bang -- 14.6.1 The age of the universe -- 14.7 Dark Matter -- 14.8 The Cosmic Microwave Background -- 14.8.1 Precision measurements of the CMB -- 14.9 The Cosmological Constant -- 14.10 Galaxy Formation -- 14.11 The Inflationary Universe -- 14.11.1 Particle horizons -- 14.11.2 Inflation -- 15 Frontiers of Physics -- 15.1 The Interpretation of Quantum Mechanics -- 15.1.1 Schrödinger's cat and Wigner's friend. , 15.1.2 The many-worlds interpretation.