5.4 Boundary conditions . 54 5.5 Examples of Magnetic Boundary value Problems........... 5.6 Energy and Magnetic Materials 57 5.7 Models of Xm············· 58 5.8 Faraday's Law.....············· 61 5.9 Inductance.···· 62 5.10 Conductivity and the Quasi-static approximation 64 6 Maxwell's Equations 66 6.1 Ampere-Maxwell Equation in electromagnetic materials............ 66 6.2 Energy and Momentum and Their Conservation ............... 67 6.3 Solving Maxwell's equations with Green Functions .............. 69 6.4 Fields with Harmonic Time Dependence............... 70 6.5 The Dirac Monopole......·..·...·. 72 6.6 Symmetries of Maxwell Equations...... 74 7 Electromagnetic Plane Waves 77 7.1 Reflection and Refraction at a Plane Interface........... 78 7.2 Brewster's Angle.························ 81 7.3 Total Internal Reflection................···....· 81 7.4 Action Principle for Maxwell's Equations.... 81 8 Lorentz Invariance and Special Relativity 83 8.1 Space-time symmetries of the wave equation... 83 8.2 Einstein's Insights........····..······· 84 8.3 Some Kinematical Aspects of Lorentz transformations..··········. 85 8.4 Space-time Tensors and their Transformation Laws 87 8.5 Lorentz covariance of Maxwell's equations................... 90 8.6 Action Principles..·.··.··········· 95 8.7 Some particle motions in electromagnetic fields..... 96 8.8 Electrodynamics of a Scalar Field...... 100 8.9 Lorentz Invariant Superconductivity:The Higgs Mechanism·..····. 104 9 Propagation of Plane waves in Materials 109 9.1 Oscillator model for frequency dependence of a dielectric........... 109 9.2 Conductivity...· 110 9.3 Plasmas and the lonosphere 111 9.4 Group Velocity...·....·. 113 9.5 Causality and Dispersion Relations.·.······.,···· 114 9.6 Causal Propagation.······················· 117 2 ©2010 by Charles Thorn5.4 Boundary conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 5.5 Examples of Magnetic Boundary value Problems . . . . . . . . . . . . . . . . 54 5.6 Energy and Magnetic Materials . . . . . . . . . . . . . . . . . . . . . . . . . 57 5.7 Models of χm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 5.8 Faraday’s Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 5.9 Inductance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 5.10 Conductivity and the Quasi-static approximation . . . . . . . . . . . . . . . 64 6 Maxwell’s Equations 66 6.1 Ampere-Maxwell Equation in electromagnetic materials . . . . . . . . . . . . 66 6.2 Energy and Momentum and Their Conservation . . . . . . . . . . . . . . . . 67 6.3 Solving Maxwell’s equations with Green Functions . . . . . . . . . . . . . . . 69 6.4 Fields with Harmonic Time Dependence . . . . . . . . . . . . . . . . . . . . 70 6.5 The Dirac Monopole . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 6.6 Symmetries of Maxwell Equations . . . . . . . . . . . . . . . . . . . . . . . . 74 7 Electromagnetic Plane Waves 77 7.1 Reflection and Refraction at a Plane Interface . . . . . . . . . . . . . . . . . 78 7.2 Brewster’s Angle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 7.3 Total Internal Reflection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 7.4 Action Principle for Maxwell’s Equations . . . . . . . . . . . . . . . . . . . . 81 8 Lorentz Invariance and Special Relativity 83 8.1 Space-time symmetries of the wave equation . . . . . . . . . . . . . . . . . . 83 8.2 Einstein’s Insights . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 8.3 Some Kinematical Aspects of Lorentz transformations . . . . . . . . . . . . . 85 8.4 Space-time Tensors and their Transformation Laws . . . . . . . . . . . . . . 87 8.5 Lorentz covariance of Maxwell’s equations . . . . . . . . . . . . . . . . . . . 90 8.6 Action Principles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 8.7 Some particle motions in electromagnetic fields . . . . . . . . . . . . . . . . . 96 8.8 Electrodynamics of a Scalar Field . . . . . . . . . . . . . . . . . . . . . . . . 100 8.9 Lorentz Invariant Superconductivity: The Higgs Mechanism . . . . . . . . . 104 9 Propagation of Plane waves in Materials 109 9.1 Oscillator model for frequency dependence of a dielectric . . . . . . . . . . . 109 9.2 Conductivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 9.3 Plasmas and the Ionosphere . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 9.4 Group Velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 9.5 Causality and Dispersion Relations . . . . . . . . . . . . . . . . . . . . . . . 114 9.6 Causal Propagation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 2 c 2010 by Charles Thorn