Classical Field Theory

Fields and Transformation Laws 1(16) Rotational Covariance 1(4) Lorentz Covariance 5(8) Scalar, Vector, and Tensor Fields 13(4) The Principle of Stationary Action 17(9) Lagrangian Mechanics of Point Particles 17(3) The Continuum Limit for Mass Points on Strings 20(6) Some General Features of Classical Field Theory 26(10) The Formulation of a Classical Field Theory 26(3) Conserved Currents 29(4) Conservation of Momentum and Energy 33(3) The Mechanics of Fluids 36(20) Description of Fluid Motion 36(5) Fluid Dynamics 41(1) The Energy-Momentum Tensor 42(4) The Internal Energy Function 46(2) Use of Momentum Conservation Equations as Equations of Motion 48(1) The Circulation Theorem 49(4) Sound Waves 53(3) The Mechanics of Elastic Solids 56(17) The Lagrangian and the Deformation Matrix 56(5) The Momentum Tensor 61(1) Boundary Conditions 62(6) Incompressible Materials 68(5) Special Types of Solids 73(12) Hooke's Law 73(4) Isotropic Materials 77(2) Isotropic Hooke's Law Materials 79(1) Sound Propagation in a Hooke's Law Solid 80(5) The Nonrelativistic Approximation 85(10) The Lagrangian 85(2) Energy and Momentum 87(1) Galilean Invariance 88(7) The Electromagnetic Field 95(6) Fields and Potentials 95(2) The Lagrangian 97(1) The Electric Field Coupled to Matter 97(4) Further General Properties of Field Theories 101(31) Noether's Theorem 101(7) Lorentz Invariance and Angular Momentum 108(4) Physical Interpretation of the Angular Momentum Tensor 112(4) The Symmetrized Momentum Tensor 116(4) The Symmetrized Momentum Tensor in Electrodynamics 120(3) A Symmetrized Momentum Tensor for Nonrelativistic Systems 123(1) The Limitations of Hamilton's Principle 124(8) Electromagnetically Polarized Materials 132(39) Sources of the Electromagnetic Field in Matter 132(8) The Electromagnetic Field-Dipole-Moment Interaction 140(1) The Matter-Dipole-Moment Interaction 141(6) The Momentum Tensor 147(6) Use of the Momentum Tensor 153(5) Piezoelectric Crystals 158(3) Perfectly Conducting Fluids 161(10) Gravity 171(36) General Covariance 171(11) The Lagrangian 182(7) The Equations of Motion for the Basic Fields 189(1) The Equations of Motion for gμv' 190(6) The Newtonian Limit 196(3) Gravitational Waves and Their Effect on Matter 199(8) Momentum Conservation in General Relativity 207(19) The Bianchi Identities and Θμvv = 0 208(2) The General Covariance Identities 210(6) Gauss' Law for Conserved Quantities 216(3) Momentum of the Gravitational Field 219(3) Θμv and the ``Symmetrized Momentum Tensor,'' 222(4) Dissipative Processes 226(29) Entropy and the Second Law of Thermodynamics 226(2) Dissipative Forces in a Gas 228(4) Entropy Flow and the Entropy Inequality 232(1) The Structure of the Dissipative Momentum Tensor 233(5) Dissipative Processes in a Fluid Dielectric 238(17) Index 255