Cover -- Half-title -- Title -- Copyright -- Dedication -- Contents -- Preface -- Part I Fundamentals -- 1 From Pythagoras to spacetime geometry -- Hands-on exercise: measuring the lengths of lines -- 1.1 Pythagoras and the measurement of space -- 1.2 The differential version, in D dimensions -- 1.3 Rotations preserve the Euclidean metric -- 1.4 Infinitesimal rotations -- 1.5 Could a line element include time? -- 1.6 The Lorentz transformation -- Exercises -- 2 Light surprises everyone -- Hands-on exercise: wave and particle properties -- 2.1 Conflicting ideas about space and light -- 2.2 Maxwell's transverse undulations -- 2.3 Galilean relativity and the ether -- 2.4 The Michelson-Morley experiment -- 2.5 Einstein ponders electromagnetism and relativity -- 2.6 Einstein's two postulates -- Implications of new theory -- Relativity of simultaneity -- Time dilation -- Length contraction -- 2.7 From light waves to spacetime geometry -- Exercises -- 3 Elements of spacetime geometry -- Hands-on exercise: manifolds and coordinate patches -- 3.1 Space and spacetime -- Coordinates in space -- Coordinates in spacetime -- The pole in the barn -- 3.2 Vectors on a manifold -- Properties of a vector space -- The tangent space -- The inner product and the metric -- Vectors and coordinate transformations -- 3.3 Vectors in spacetime -- Timelike vectors -- Velocity and momentum in spacetime -- Lorentz boost of velocity -- Null vectors -- Spacelike vectors -- 3.4 Tensors and forms -- From one forms to p forms -- Lorentz transformation of forms -- What is a tensor? -- Lorentz transformation of tensors -- 3.5 The Principle of Relativity as a geometric principle -- Exercises -- 4 Mechanics in spacetime -- Hands-on exercise: review of Galilean relativity -- 4.1 Equations of motion in spacetime -- Newton's equation and relativity -- Relativistic acceleration.

Relativistic force -- World line of a free particle -- World line of a uniformly accelerated object -- 4.2 Momentum and energy in spacetime -- Energy and momentum of a massless object -- Units of mass and energy -- 4.3 Energy and momentum conservation in spacetime -- The nonrelativistic case -- The relativistic case -- 4.4 Relativistic kinematics -- Photons and charged particles -- Compton scattering -- Virtual photons -- Pair creation and annihilation -- Particle decay -- Particle collisions in accelerators -- 4.5 Fission, fusion, and E = Mc2 -- A new world order is born -- Nuclear fission -- Nuclear fusion -- 4.6 Rigid body mechanics -- Exercises -- 5 Spacetime physics of fields -- Hands-on exercise: the stress tensor of a tub of water -- 5.1 What is a field? -- The rise of classical field theory -- Fields in spacetime -- 5.2 Differential calculus in spacetime -- The Laplace equation in spacetime -- The exterior derivative -- The Lie derivative -- Killing vectors and conservation laws -- 5.3 Integral calculus in spacetime -- Volumes and forms -- Integration of forms -- Stokes's theorem -- 5.4 Continuous systems in spacetime -- Energy and momentum -- The stress tensor for a perfect fluid -- Stress tensor for pointlike particles -- Stokes's theorem and momentum conservation -- Energy conservation for a perfect fluid -- Angular momentum -- 5.5 Electromagnetism -- The Faraday tensor -- The Maxwell tensor -- Gaussian units and relativity -- The vector potential -- The electromagnetic stress tensor -- Electromagnetic waves -- Motion of charged particles in spacetime -- Conservation of energy and momentum -- Electromagnetism in higher dimensions -- Magnetic monopoles -- 5.6 What about the gravitational field? -- Exercises -- 6 Causality and relativity -- Hands-on exercise -- 6.1 What is time? -- Back to Pythagoras -- Time along a world line.

Time as a spacelike hypersurface -- 6.2 Causality and spacetime -- Time, space and light -- Null hypersurfaces in spacetime -- The causal regions of an event -- The causal regions of an object -- The initial value problem in spacetime -- Causality and the wave equation -- Exercises -- Part II Advanced Topics -- 7 When quantum mechanics and relativity collide -- 7.1 Yet another surprise about light -- The conflict between classical electrodynamics and thermodynamics -- The quantum understanding of light begins -- 7.2 The Schrödinger equation is not covariant -- From classical mechanics to the Schrödinger equation -- Time and space in quantum mechanics -- When is the Schrödinger equation a good approximation? -- The harmonic oscillator -- 7.3 Some new ideas from the Klein-Gordon equation -- The Klein-Gordon equation -- A plane wave solution -- Particles and antiparticles -- 7.4 The Dirac equation and the origin of spin -- The massless Dirac equation in two dimensions -- The massive Dirac equation in two dimensions -- The massive Dirac equation in four dimensions -- Spin 1/2 particles -- 7.5 Relativity demands a new approach -- The Dirac sea and the prediction of antimatter -- Relativistic quantum mechanics is not a complete theory -- Particle creation and annihilation -- Particles and fields -- Microscopic causality -- 7.6 Feynman diagrams and virtual particles -- What is a virtual particle? -- Feynman diagrams for e+e- elastic scattering -- Radiative corrections -- Further developments in quantum field theory -- Exercises -- 8 Group theory and relativity -- 8.1 What is a group? -- Simple examples of groups -- The four properties that define a group -- Group representations -- 8.2 Finite and infinite groups -- Permutation groups -- Unitary and orthogonal groups -- 8.3 Rotations form a group -- Infinitesimal rotations and the SO(3) algebra.

Representation by differential operators -- The relationship between SO(3) and SU(2) -- Spinor representations -- Rotations in higher dimensions -- 8.4 Lorentz transformations form a group -- The Lorentz group has four components -- The difference between space and spacetime rotations -- Infinitesimal Lorentz transformations -- 8.5 The Poincaré group -- Space and time translations -- Commutators of translations and rotations -- Representations of the Poincaré group -- Exercises -- 9 Supersymmetry and superspace -- 9.1 Bosons and fermions -- Bosons -- Fermions -- Spin and statistics -- Coleman-Mandula theorem -- 9.2 Superspace -- Grassmann numbers and Grassmann algebras -- Odd and even functions -- Superspace -- 9.3 Supersymmetry transformations -- Supertranslations -- The commutator of two supertranslations -- Differential operators on superspace -- Supersymmetry generators and the supersymmetry algebra -- From Poincaré to super-Poincaré -- 9.4 N = 1 supersymmetry in four dimensions -- Two-component and four-component notation -- 9.5 Massless representations -- Chiral supermultiplets -- Vector supermultiplets -- The gravity supermultiplet -- Exercises -- 10 Looking onward -- 10.1 Relativity and gravity -- Basic concepts of general relativity -- The classical experimental tests -- Black holes -- Gravitational radiation -- The Universe -- 10.2 The standard model of elementary particle physics -- Yang-Mills fields -- Quarks and leptons -- The quarks -- The antiquarks -- The leptons -- The antileptons -- The Higgs mechanism -- Why there must be more -- 10.3 Supersymmetry -- The gauge hierarchy problem -- The minimal supersymmetric standard model -- Charginos -- Neutralinos -- R parity and the lightest supersymmetric particle -- Grand unification -- 10.4 The relativistic string -- World-line description of a point particle.

World-sheet description of a relativistic string -- Quantization -- Perturbation theory -- 10.5 Superstrings -- Supersymmetric strings -- Five superstring theories -- Compactification of extra dimensions -- 10.6 Recent developments in superstring theory -- T duality -- S duality -- M theory -- D-branes -- Black hole entropy -- AdS/CFT duality -- 10.7 Problems and prospects -- Find a complete formulation of the theory -- Understand the cosmological constant -- Find all quantum vacua of the theory -- Understand black holes and spacetime singularities -- Understand time-varying solutions -- Develop mathematical tools and concepts -- Exercises -- Appendix 1 Where do equations of motion come from? -- A1.1 Classical mechanics -- A1.2 Classical field theory -- Symmetries and conservation laws -- A1.3 Quantization -- Operator formalism -- Feynman path integral -- The problem of constraints -- Appendix 2 Basic group theory -- Appendix 3 Lie groups and Lie algebras -- Appendix 4 The structure of super Lie algebras -- References -- Index.