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1 | (6) |
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2 The History of Views on Charges, Currents and the Electromagnetic Field |
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7 | (42) |
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2.1 The PreMaxwellian Era, Luminiferous Ether and Action-at-a-Distance |
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8 | (5) |
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2.1.1 Ether and Action-at-a-Distance |
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8 | (1) |
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2.1.2 Corpuscular and Wave Theories |
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9 | (2) |
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11 | (2) |
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2.2 Maxwell's Field Theory |
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13 | (3) |
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16 | (4) |
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2.4 Problems with Elementary Charge Treated as a Point |
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20 | (1) |
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2.5 The Concept of an Extended Charge |
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21 | (2) |
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2.6 Poincare's Contribution |
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23 | (1) |
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2.7 Planck's Insights on Black-Body Radiation and Energy Quanta |
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24 | (2) |
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26 | (7) |
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2.8.1 Ether and Action-at-Distance |
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27 | (2) |
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2.8.2 Problems with Maxwell's Theory and Quantization of Electromagnetic Radiation |
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29 | (2) |
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31 | (1) |
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31 | (1) |
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2.8.5 Material Points Versus Continuous Fields |
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32 | (1) |
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2.9 De Broglie's Theory of Phase Waves |
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33 | (3) |
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2.10 Schrodinger Wave Mechanics |
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36 | (4) |
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2.11 De Broglie-Bohm Theory |
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40 | (5) |
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2.12 Continuum Theories and Atomicity |
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45 | (1) |
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2.13 Quantum Electrodynamics (QED) |
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46 | (3) |
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3 The Neoclassical Field Theory of Charged Matter: A Concise Presentation |
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49 | (40) |
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3.1 Point Charges in Classical Electromagnetic Theory |
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52 | (3) |
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3.2 The Concept of Balanced Charge, the First Glimpse of the Theory |
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55 | (3) |
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3.3 Localization of Balanced Charges and the Nonlinearity |
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58 | (2) |
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3.4 Lagrangian, Field Equations and Conservation Laws for Interacting Balanced Charges |
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60 | (4) |
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3.5 The Concept of Wave-Corpuscle |
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64 | (10) |
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3.5.1 The Wave-Corpuscle Versus the WKB Quasiclassical Approximation |
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65 | (3) |
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3.5.2 The Wave-Corpuscle as an Approximation |
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68 | (1) |
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3.5.3 Coexistence of Wave and Particle Properties in a Wave-Corpuscle |
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69 | (3) |
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3.5.4 A Hypothetical Scenario for the Davisson-Germer Experiment |
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72 | (2) |
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3.6 Particle-Like Dynamics |
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74 | (4) |
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3.6.1 Derivation of Newton's Law from the Field Conservation Laws |
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74 | (1) |
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3.6.2 Derivation of the Relativistic Law of Motion and Einstein's Formula E = Mc2 |
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75 | (3) |
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78 | (5) |
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3.7.1 The Planck-Einstein Formula and the Logarithmic Nonlinearity |
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79 | (2) |
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81 | (2) |
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3.8 Comparison with Quantum Mechanics and Classical Electrodynamics |
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83 | (6) |
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Part I Classical Electromagnetic Theory and Special Relativity |
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89 | (66) |
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4.1 The Maxwell Equations in Tensorial Form |
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91 | (3) |
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4.1.1 Frame Transformation Formulas |
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93 | (1) |
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4.2 The Green Functions for the Maxwell Equations |
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94 | (7) |
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4.2.1 Point Charges and the Lienard-Wiechert Potential |
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97 | (2) |
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4.2.2 Radiation Fields and Radiated Energy |
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99 | (2) |
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5 Dipole Approximation for Localized Distributed Charges |
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101 | (6) |
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101 | (2) |
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5.2 Dipole Elementary Currents |
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103 | (4) |
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6 The Minkowski Four-Dimensional Spacetime and Relativistic Kinematics |
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107 | (12) |
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6.1 The Minkowski Four-Dimensional Spacetime |
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107 | (1) |
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6.2 The Lorentz Transformation |
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108 | (4) |
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6.2.1 Spinorial Form of the Lorentz Transformations |
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110 | (2) |
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6.3 Relativistic Kinematics |
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112 | (1) |
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6.4 Point Charges in an External Electromagnetic Field |
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113 | (6) |
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6.4.1 Point Charges and the Lorentz-Abraham Model |
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115 | (1) |
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6.4.2 Forces and Torques Exerted on Localized Distributed Charges |
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116 | (1) |
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6.4.3 Angular Momentum and Gyromagnetic Ratio |
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117 | (2) |
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7 Longitudinal and Transversal Fields |
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119 | (8) |
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7.1 The Helmholtz Decomposition of the Potential Form of the Maxwell Equations |
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119 | (6) |
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7.1.1 Scalar Potentials of Longitudinal Fields |
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121 | (3) |
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7.1.2 Gauge Transformations in Scalar Potential Form |
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124 | (1) |
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7.2 Maxwell's Equations Decomposition |
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125 | (2) |
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8 Non-relativistic Quasistatic Approximations |
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127 | (14) |
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8.1 Galilean Electromagnetism |
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128 | (3) |
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8.2 Electroquasistatics (EQS) |
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131 | (3) |
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8.3 Darwin's Quasistatics Approximation |
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134 | (3) |
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8.4 The First Non-relativistic Approximation |
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137 | (1) |
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8.5 The Second Non-relativistic Approximation |
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138 | (3) |
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9 Electromagnetic Field Lagrangians |
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141 | (14) |
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9.1 Energy-Momentum Tensor for Electromagnetic Field |
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143 | (1) |
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144 | (1) |
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145 | (3) |
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9.4 Non-relativistic Quasistatic EM Lagrangians and the Field Equations |
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148 | (7) |
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9.4.1 Electroquasistatics and Darwin's Lagrangians |
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148 | (1) |
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9.4.2 The First Non-relativistic EM Field Lagrangian and the Field Equations |
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149 | (1) |
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9.4.3 The Second Non-relativistic EM Field Lagrangian and the Field Equations |
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150 | (5) |
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Part II Classical Field Theory |
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10 Variational Principles, Lagrangians, Field Equations and Conservation Laws |
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155 | (26) |
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10.1 The Action Integral and the Euler-Lagrange Field Equations |
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156 | (3) |
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10.2 Symmetry Transformations of a Lagrangian and Its Action Integral |
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159 | (4) |
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10.2.1 Symmetry Transformations for the Poincare Group |
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160 | (1) |
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10.2.2 In variance of the Action Integral |
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161 | (2) |
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10.3 Conservation Laws for Noether's Currents |
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163 | (2) |
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10.4 Canonical Energy-Momentum Tensor |
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165 | (2) |
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10.5 The Symmetric Energy-Momentum Tensor |
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167 | (2) |
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10.6 Conserved Quantities |
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169 | (2) |
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10.7 Symmetries and Conservation Laws Revisited |
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171 | (6) |
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10.7.1 Symmetry Transformations and Noether's Conserved Currents |
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172 | (2) |
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10.7.2 The Symmetric Energy-Momentum Tensor (EnMT) and Angular Momentum |
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174 | (3) |
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10.8 Examples of the Classical Field Theories |
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177 | (4) |
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10.8.1 Compressional Waves in Non-viscous Compressible Fluid |
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177 | (2) |
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10.8.2 The Lagrangian for an Abstract Schrodinger Equation |
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179 | (2) |
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11 Lagrangian Field Formalism for Charges Interacting with EM Fields |
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181 | (38) |
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11.1 Many Charges Interacting with Electromagnetic Fields: General Aspects |
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182 | (6) |
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11.1.1 Lagrangian and Field Equations |
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183 | (3) |
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11.1.2 Field Equations for Elementary EM Fields |
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186 | (2) |
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11.2 Gauge Invariance and Symmetric Energy-Momentum Tensors |
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188 | (6) |
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11.2.1 Symmetries of the Lagrangian |
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188 | (2) |
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11.2.2 The Continuity Equation and Preservation of the Lorentz Gauge |
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190 | (2) |
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11.2.3 Source Currents in Maxwell's Equations and Charge Conserved Currents |
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192 | (1) |
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11.2.4 The Additivity Property of Currents and Fields |
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193 | (1) |
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11.3 Partition of Energy-Momentum for Many Interacting Fields |
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194 | (1) |
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11.4 Partition of Canonical Energy-Momentum |
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194 | (2) |
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11.5 Partition of the EnMT Conservation Law |
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196 | (11) |
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11.5.1 Partition of the Conservation Law for the Total Canonical EnMT |
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197 | (2) |
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11.5.2 Symmetrized Energy-Momenta and Conservation Laws for Every Charge |
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199 | (2) |
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11.5.3 The Energy-Momentum Tensor for EM Fields |
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201 | (4) |
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11.5.4 Total Symmetrized Energy Momentum |
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205 | (1) |
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11.5.5 Cancellation of Self-interaction in Energy-Momentum Conservation Laws |
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206 | (1) |
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11.6 Lagrangian Field Formalism for the Klein-Gordon Equation |
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207 | (4) |
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11.6.1 The Energy-Momentum Tensor and Conservation Laws for the NKG Equation |
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209 | (1) |
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11.6.2 The Linear Klein-Gordon Equation |
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210 | (1) |
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11.7 The Frequency Shifted Lagrangian |
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211 | (1) |
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11.8 Lagrangian Field Formalism for the Nonlinear Schrodinger Equation |
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212 | (7) |
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11.8.1 The Energy-Momentum Tensor for the NLS |
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213 | (2) |
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11.8.2 Galilean Gauge-In variance |
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215 | (4) |
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12 Lagrangian Field Formalism for Balanced Charges |
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219 | (10) |
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12.1 Relativistic Balanced Charges |
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219 | (2) |
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12.2 Non-relativistic Balanced Charges |
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221 | (6) |
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12.2.1 Derivation of the Non-relativistic Approximation |
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225 | (2) |
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12.3 Balanced Charges Gauge Invariance |
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227 | (2) |
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13 Lagrangian Field Formalism for Dressed Charges |
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229 | (10) |
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13.1 Relativistic Lagrangian Formalism for Interacting Dressed Charges |
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229 | (3) |
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13.1.1 A Single Relativistic Dressed Charge in an External Electromagnetic Field |
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231 | (1) |
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13.2 Non-relativistic Lagrangian Formalism for Interacting Dressed Charges |
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232 | (7) |
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13.2.1 Energy-Momentum Tensors for Non-relativistic Dressed Charges |
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234 | (5) |
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Part III The Neoclassical Theory of Charges |
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14 Rest and Time-Harmonic States of a Charge |
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239 | (40) |
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14.1 Rest States of a Non-relativistic Balanced Charge |
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240 | (2) |
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14.2 The Charge Normalization Condition |
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242 | (1) |
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14.3 Ground State and the Nonlinearity |
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243 | (6) |
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245 | (1) |
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14.3.2 Examples of the Nonlinearity |
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246 | (3) |
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14.4 Relativistic Time-Harmonic States of a Balanced Charge |
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249 | (7) |
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14.4.1 Time-Harmonic States for the Logarithmic Nonlinearity |
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252 | (2) |
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14.4.2 Electric Potential Proximity to the Coulomb's Potential |
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254 | (2) |
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14.5 The Rest State of a Non-relativistic Dressed Charge |
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256 | (9) |
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14.5.1 Nonlinear Self-Interaction of a Dressed Charge and Its Basic Properties |
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257 | (3) |
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14.5.2 Examples of Nonlinearities for a Dressed Charge |
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260 | (3) |
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14.5.3 The Energy Related Spatial Scale |
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263 | (2) |
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14.6 The Rest Slate of a Relativistic Dressed Charge |
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265 | (7) |
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14.6.1 Relativistic and Non-relativistic Resting Charges |
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268 | (1) |
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14.6.2 The Energy-Momentum Tensor and Forces at Equilibrium of a Dressed Charge |
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269 | (3) |
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14.7 Variational Characterization of Static and Time-Harmonic States |
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272 | (2) |
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14.8 Energy Partition for Rest and Time-Harmonic States |
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274 | (5) |
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15 Uniform Motion of a Charge |
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279 | (12) |
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15.1 Freely Moving Non-relativistic Balanced Charges |
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279 | (4) |
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15.1.1 Point and Wave Attributes of Wave Corpuscles |
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280 | (1) |
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15.1.2 Plane Waves, Wave Packets and Dispersion Relations |
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281 | (2) |
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15.2 Uniform Motion of a Relativistic Balanced Charge |
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283 | (2) |
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15.3 A Single Free Non-relativistic Dressed Charge |
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285 | (1) |
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15.4 A Relativistic Dressed Charge in Uniform Motion |
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286 | (5) |
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15.4.1 Properties of a Free Dressed Charge |
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287 | (4) |
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16 Accelerating Wave-Corpuscles |
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291 | (32) |
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16.1 Wave-Corpuscle Preservation in Accelerated Motion |
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293 | (11) |
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16.1.1 A Criterion for Shape Preservation |
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294 | (2) |
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16.1.2 Trajectory and Phase of a Wave-Corpuscle |
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296 | (3) |
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16.1.3 Universality of Dynamic Balance Conditions |
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299 | (1) |
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16.1.4 Wave-Corpuscle Motion in the Electric Field |
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299 | (1) |
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16.1.5 Wave-Corpuscles in the EM Field |
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300 | (4) |
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16.2 Particle and Wave Features in Accelerated Motion of a Wave-Corpuscle |
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304 | (3) |
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16.2.1 The de Broglie Wavevector |
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304 | (2) |
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16.2.2 The Dispersion Relation and Group Velocity |
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306 | (1) |
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16.3 Wave-Corpuscles in a General Field as an Approximation |
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307 | (8) |
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16.3.1 Estimate of the Discrepancy |
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309 | (2) |
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16.3.2 Perturbed Wave-Corpuscles |
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311 | (2) |
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16.3.3 On Stability of the Perturbed Form Factor |
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313 | (2) |
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16.4 Wave-Corpuscle for an Accelerating Balanced Charge |
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315 | (8) |
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16.4.1 Current, Charge, Energy and Momentum for a Wave-Corpuscle |
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316 | (1) |
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16.4.2 The Planck-Einstein Relation for a Wave-Corpuscle |
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317 | (1) |
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16.4.3 The Vector Potential for a Non-relativistic Wave Corpuscle |
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318 | (3) |
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16.4.4 Wave-Corpuscle for an Accelerating Dressed Charge |
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321 | (2) |
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17 Interaction Theory of Balanced Charges |
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323 | (50) |
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17.1 Theory of Non-relativistic Balanced Charges |
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324 | (2) |
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17.1.1 A Charge Singled Out from the Non-relativistic System |
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325 | (1) |
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17.1.2 Exact Wave-Corpuscle Solutions: Accelerating Solitons |
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325 | (1) |
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17.2 Non-relativistic Macroscopic Dynamics of Balanced Charges |
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326 | (9) |
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17.2.1 Individual Momenta System |
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326 | (1) |
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17.2.2 The Ehrenfest Theorem for Interacting Balanced Charges |
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327 | (2) |
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17.2.3 Newtonian Mechanics as an Approximation |
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329 | (1) |
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17.2.4 Point Mechanics of Balanced Charges via Wave-Corpuscles |
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330 | (2) |
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17.2.5 A Discrepancy Estimate for the Construction |
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332 | (2) |
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334 | (1) |
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17.3 Close Interaction of Balanced Charges |
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335 | (1) |
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17.4 Multiharmonic Solutions for a System of Many Charges |
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335 | (7) |
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17.4.1 The Planck-Einstein Frequency-Energy Relation and the Logarithmic Nonlinearity |
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338 | (4) |
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17.5 A Two Particle Hydrogen-Like System |
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342 | (8) |
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17.5.1 The Electron-Proton System as a Hydrogen Atom Model |
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342 | (4) |
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17.5.2 Reduction to One Charge in the Coulomb Field |
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346 | (4) |
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17.6 Relativistic Balanced Charge Theory |
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350 | (23) |
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17.6.1 Relativistic Field Equations for Balanced Charges |
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350 | (3) |
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17.6.2 A Relativistic Localized Distributed Charge as a Particle |
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353 | (14) |
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17.6.3 The Relativistic Interaction of Balanced Charges |
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367 | (3) |
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17.6.4 A Relativistic Hydrogen Atom Model |
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370 | (3) |
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18 Relation to Quantum Mechanical Models and Phenomena |
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373 | (16) |
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18.1 Comparison with the Schrodinger Wave Theory |
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373 | (10) |
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18.1.1 Uncertainty Relations |
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375 | (4) |
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18.1.2 Quantum Statistics and Non-locality |
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379 | (2) |
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18.1.3 Relation to Hidden Variables Theories |
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381 | (1) |
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18.1.4 Comparative Summary of the Neoclassical Theory and the Schrodinger Wave Mechanics |
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382 | (1) |
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18.2 The Size of a Free Electron as a New Fundamental Scale |
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383 | (6) |
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18.2.1 Electron Field Emission Physics |
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384 | (1) |
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384 | (2) |
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18.2.3 Finite-Size Particles or Clouds in Plasma Physics |
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386 | (3) |
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19 The Theory of Electromagnetic Interaction of Dressed Charges |
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389 | (16) |
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19.1 The Ehrenfest Theorem for Non-relativistic Dynamics of the Charge Center |
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390 | (3) |
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19.2 Many Interacting Dressed Charges |
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393 | (2) |
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19.2.1 The Ehrenfest Theorem for Dynamics of Many Interacting Dressed Charges |
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393 | (2) |
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19.3 Mechanics of Localized Charge Centers as an Approximation |
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395 | (1) |
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19.4 Point Mechanics of Dressed Charges Via Wave-Corpuscles |
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396 | (1) |
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19.5 A Hydrogen Atom Model |
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397 | (4) |
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19.6 The Relativistic Theory of Interacting Dressed Charges |
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401 | (1) |
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401 | (1) |
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19.7 Dressed Charge Equations in Dimensionless Form and the Non-relativistic Limit |
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402 | (3) |
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20 Comparison of EM Aspects of Dressed and Balanced Charges Theories |
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405 | (18) |
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20.1 Lagrangian Formalism for Dressed Charges Versus Balanced Charges |
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405 | (1) |
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20.2 BEM Theory (Reduced Balanced Charge Theory) |
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406 | (17) |
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20.2.1 BEM and CEM Theories |
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407 | (1) |
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20.2.2 Individual EM Energy-Momentum Tensors |
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408 | (2) |
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20.2.3 Individual EnMT Conservation Laws |
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410 | (2) |
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20.2.4 Elementary Currents for Point Charges |
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412 | (1) |
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20.2.5 Energy Flux for a Pair of Elementary Dipoles |
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413 | (3) |
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20.2.6 The Lagrangian for Clusters of Charges |
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416 | (7) |
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Part IV The Neoclassical Theory of Charges with Spin |
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423 | (4) |
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427 | (4) |
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23 Basics of Spacetime Algebra (STA) |
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431 | (10) |
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24 The Dirac Equation in the STA |
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441 | (12) |
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443 | (5) |
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24.1.1 Electric Charge Conservation |
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444 | (3) |
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24.1.2 Energy-Momentum Conservation |
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447 | (1) |
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24.2 Free Electron Solutions to the Dirac Equation |
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448 | (5) |
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25 The Basics of the Neoclassical Theory of Charges with Spin 1/2 |
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453 | (8) |
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456 | (5) |
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25.1.1 Charge and Current Densities |
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456 | (2) |
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25.1.2 Gauge Invariant Energy-Momentum Tensor |
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458 | (3) |
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26 Neoclassical Free Charge with Spin |
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461 | (10) |
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461 | (2) |
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26.2 Solutions to the Spinor Field Equation |
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463 | (1) |
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26.3 Charge and Current Densities |
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464 | (2) |
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26.4 Energy-Momentum Density |
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466 | (5) |
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27 Neoclassical Solutions: Interpretation and Comparison with the Dirac Theory |
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471 | (6) |
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27.1 The Gyromagnetic Ratio and Currents |
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474 | (1) |
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27.2 The Energies and Frequencies |
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474 | (1) |
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475 | (2) |
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28 Clifford and Spacetime Algebras |
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477 | (14) |
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28.1 Isometries, Reflections, Versors and Rotors |
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478 | (2) |
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28.2 Clifford Algebra Bases |
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480 | (1) |
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28.3 Inner and Outer Product Properties |
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481 | (2) |
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483 | (2) |
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28.5 The Commutator Product and Bivectors |
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485 | (2) |
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28.6 Pseudoscalar, Duality and the Cross Product |
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487 | (4) |
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491 | (8) |
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29.1 Definition and Basic Properties of Multivector Derivatives |
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491 | (3) |
|
29.2 The Vector Derivative and Its Basic Properties |
|
|
494 | (2) |
|
29.3 Examples of Multivector Derivatives |
|
|
496 | (3) |
|
30 Relativistic Concepts in the STA |
|
|
499 | (20) |
|
30.1 Inertial Systems and the Spacetime Split |
|
|
499 | (4) |
|
30.2 Multivector and Bivector Spacetime Split |
|
|
503 | (2) |
|
30.3 Electromagnetic Field Spacetime Split |
|
|
505 | (1) |
|
30.4 Lorentz Transformations and Their Rotors |
|
|
506 | (6) |
|
30.4.1 Lorentz Rotor Spacetime Split |
|
|
508 | (2) |
|
30.4.2 Lorentz Boosts and Spacetime Splits |
|
|
510 | (2) |
|
30.4.3 Field Transformations |
|
|
512 | (1) |
|
30.5 Active and Passive Transformations |
|
|
512 | (2) |
|
30.6 The Motion Equation of a Point Charged Particle |
|
|
514 | (1) |
|
30.7 Spinor Point Particle Mechanics |
|
|
515 | (4) |
|
31 Electromagnetic Theory in the STA |
|
|
519 | (8) |
|
31.1 Electromagnetic Fields in Dielectric Media |
|
|
520 | (3) |
|
31.2 Time-Harmonic Solutions to the Maxwell Equation in Vacuum |
|
|
523 | (4) |
|
32 The Wave Function and Local Observables in the STA |
|
|
527 | (4) |
|
33 Multivector Field Theory |
|
|
531 | (10) |
|
33.1 Transformations Laws |
|
|
531 | (1) |
|
33.2 Lagrangian Treatment and Conservation Laws for Multivector Fields |
|
|
532 | (3) |
|
33.3 The Symmetric Energy-Momentum Tensor |
|
|
535 | (6) |
|
Part V Mathematical Aspects of the Theory of Distributed Elementary Charges |
|
|
|
34 Trajectories of Concentration |
|
|
541 | (72) |
|
34.1 Derivation of Non-relativistic Point Dynamics for Localized Solutions of the NLS |
|
|
542 | (18) |
|
34.1.1 Localized NLS Equations |
|
|
546 | (5) |
|
34.1.2 Properties of Concentrating Solutions of NLS |
|
|
551 | (3) |
|
34.1.3 Derivation of Newton's Equation for the Trajectory of Concentration |
|
|
554 | (2) |
|
34.1.4 Wave-Corpuscles as Concentrating Solutions |
|
|
556 | (4) |
|
34.2 Concentration of Asymptotic Solutions |
|
|
560 | (6) |
|
34.2.1 Point Trajectories as Trajectories of Asymptotic Concentration |
|
|
563 | (3) |
|
34.3 Trajectories of Concentration in Relativistic Field Dynamics |
|
|
566 | (4) |
|
34.3.1 Rigorous Derivation of Einstein's Formula for a Balanced Charge |
|
|
566 | (4) |
|
34.4 Basic Properties of the Klein-Gordon Equation |
|
|
570 | (2) |
|
34.4.1 Nonlinearity Properties |
|
|
570 | (1) |
|
34.4.2 Conservation Laws for the Klein-Gordon Equation |
|
|
571 | (1) |
|
34.5 Relativistic Dynamics of Localized Solutions |
|
|
572 | (15) |
|
34.5.1 Concentrating Solutions of the NKG Equation |
|
|
572 | (7) |
|
34.5.2 Properties of Concentrating Solutions |
|
|
579 | (4) |
|
34.5.3 Proof of Theorem 34.5.1 |
|
|
583 | (4) |
|
34.6 Rectilinear Accelerated Motion of a Wave-Corpuscle |
|
|
587 | (26) |
|
34.6.1 Reduction to One Dimension |
|
|
588 | (2) |
|
34.6.2 Equation in a Moving Frame |
|
|
590 | (1) |
|
34.6.3 Equations for Auxiliary Phases |
|
|
591 | (3) |
|
34.6.4 Construction and Properties of the Auxiliary Potential |
|
|
594 | (11) |
|
34.6.5 Verification of the Concentration Conditions |
|
|
605 | (6) |
|
34.6.6 Concentration of Solutions of a Linear NKG Equation |
|
|
611 | (2) |
|
35 Energy Functionals and Nonlinear Eigenvalue Problems |
|
|
613 | (30) |
|
35.1 Properties of the NLS with Logarithmic Nonlinearity |
|
|
613 | (7) |
|
35.1.1 Gaussian Shape as a Global Minimum of Energy |
|
|
613 | (3) |
|
|
|
616 | (2) |
|
35.1.3 The Planck-Einstein Formula for Multiharmonic Solutions |
|
|
618 | (2) |
|
35.2 Mathematical Aspects of the Hydrogen Model for Balanced Charges |
|
|
620 | (23) |
|
35.2.1 The Variational Problem for a Charge in the Coulomb Field |
|
|
620 | (6) |
|
35.2.2 Nonlinear Eigenvalues for a Charge in the Coulomb Field |
|
|
626 | (17) |
|
|
|
|
36 Elementary Momentum Equation Derivation for NKG |
|
|
643 | (2) |
|
37 Fourier Transforms and Green Functions |
|
|
645 | (2) |
|
38 Splitting of a Field into Gradient and Sphere-Tangent Parts |
|
|
647 | (4) |
|
39 Hamilton-Jacobi Theory |
|
|
651 | (6) |
|
40 Point Charges in a Spatially Homogeneous Electric Field |
|
|
657 | (4) |
|
41 Statistical and Wave Viewpoints in Hamilton-Jacobi Theory |
|
|
661 | (4) |
|
42 Almost Periodic Functions and Their Time-Averages |
|
|
665 | (4) |
|
|
|
669 | (2) |
|
|
|
670 | (1) |
|
44 The Helmholtz Decomposition |
|
|
671 | (4) |
|
|
|
675 | (4) |
| References |
|
679 | (12) |
| Index |
|
691 | |
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