Preface Acknowledgments Author biographies 1 Least action 1.1 Optics 1.1.1 Snell's law 1.1.2 Complicated problems 1.1.3 Light in vacuum 1.1.4 Light in the atmosphere 1.2 Newtonian dynamics 1.2.1 Multiple coordinates 1.2.2 Example: projectile motion 1.2.3 Example 2: double pendulum 1.3 Conservation laws 1.3.1 Ignorable coordinates 1.3.2 Energy conservation 1.3.3 Example: central forces 1.3.4 Hamiltonian and energy A Calculus of variation B Mathematics of conservation laws 2 Special relativity 2.1 The postulates 2.2 Lorentz transformations 2.2.1 Time dilation 2.2.2 Lorentz contraction 2.3 An analogy to rotations 2.4 Four-vectors 2.4.1 Index convention 2.5 The laws of dynamics 2.5.1 Four-velocity 2.5.2 Four-acceleration 2.5.3 Four-momentum 2.5.4 Hypothesis for dynamical law 2.6 Physics with four-momentum 2.6.1 The Doppler effect 2.6.2 The Compton effect 2.6.3 Fixed target experiments 2.6.4 The GZK bound 2.7 Tensors 2.8 Relativistic action 2.9 Lorentz transformations and rotations II 3 Relativistic electromagnetism 3.1 Integral form of Maxwell's equations 3.1.1 Gauss' law 3.1.2 No magnetic charges 3.1.3 Faraday's law 3.1.4 Ampere's law 3.2 Differential form of Maxwell's equations 3.2.1 Maxwell's equations in differential form 3.2.2 Conservation of charge 3.2.3 The displacement current 3.3 Potentials 3.3.1 Electrostatic potential 3.3.2 The magnetic vector potential 3.3.3 A new electric potential 3.3.4 Gauge transformations 3.3.5 Maxwell's equations in Lorenz gauge 3.4 Relativistic formulation of electromagnetism 3.4.1 Four-vector current 3.4.2 Conservation of charge 3.4.3 The four-vector 3.4.4 Four vector potential 3.4.5 The electromagnetic field strength tensor 3.4.6 Lorentz transformations of electric and magnetic fields 3.4.7 The relativistic force law 3.5 The Lagrangian for a charged particle C Gauss' and Stokes' theorems C.1 Gauss' theorem C.2 Stokes' theorem D Vector identities ��݋��ӛ