Electrodynamics: A Modern Geometric Approach

Contents......Page p0006.djvu
Preface......Page p0012.djvu
1. Introduction......Page p0018.djvu
1.1. Units......Page p0019.djvu
1.2. Electromagnetic Theory and Vector Algebra......Page p0023.djvu
1.3. An Introduction to Clifford Algebras......Page p0025.djvu
1.4. Geometric Interpretations......Page p0029.djvu
1.5. Problems......Page p0045.djvu
2.1. The Spacetime Manifold......Page p0050.djvu
2.2. Lorentz Transformations......Page p0057.djvu
2.3. Spacetime Planes......Page p0062.djvu
2.4. Spacetime Rotations......Page p0068.djvu
2.5. Proper Velocity......Page p0071.djvu
2.6. Tetrads and Matrix Representations......Page p0076.djvu
2.7. Spacetime Diagrams......Page p0084.djvu
2.8. Electromagnetic Field......Page p0086.djvu
2.9. Problems......Page p0089.djvu
3. Maxwell's Equations(s)......Page p0096.djvu
3.1. Covariant Form......Page p0098.djvu
3.2. Conservation of Charge......Page p0108.djvu
3.4. Magnetic Monopoles......Page p0110.djvu
3.5. Electromagnetic Potential......Page p0112.djvu
3.6. Gauge Invariance......Page p0114.djvu
3.7. Energy and Momentum Density......Page p0115.djvu
3.8. Problems......Page p0119.djvu
4.1. Covariant Form......Page p0125.djvu
4.2. Eigenspinors......Page p0127.djvu
4.3. Invariant Planes and Directions......Page p0130.djvu
4.4. The Group SL(2,C)......Page p0134.djvu
4.5. Time Evolution of Eigenspinor......Page p0137.djvu
4.6. Thomas Precession......Page p0138.djvu
4.7. Spinorial Form of Lorentz-Force Equation......Page p0139.djvu
4.8. Motion in Constant Fields......Page p0140.djvu
4.9. Motion in Varying Fields......Page p0146.djvu
4.10. Field Momenta......Page p0150.djvu
4.11. Problems......Page p0154.djvu
5.1. Wave Equation......Page p0160.djvu
5.2. Waves in a String......Page p0162.djvu
5.3. Separation of Variables......Page p0163.djvu
5.4. Fourier Series......Page p0164.djvu
5.5. Fourier Integrals......Page p0167.djvu
5.6. Transmission Lines......Page p0173.djvu
5.7. Impedance and Reflections......Page p0175.djvu
5.8. Problems......Page p0177.djvu
6. Electromagnetic Waves in Vacuum......Page p0183.djvu
6.1. Maxwell's Equation in a Vacuum......Page p0184.djvu
6.2. Projectors......Page p0188.djvu
6.3. Directed Plane Waves and Flags......Page p0191.djvu
6.4. Monochromatic Plane Waves......Page p0194.djvu
6.5. Motion of Charges in Plane Waves......Page p0197.djvu
6.6. Monochromatic Standing Waves......Page p0202.djvu
6.7. Problems......Page p0205.djvu
7. Polarization......Page p0211.djvu
7.1. Polarization of Monochromatic Waves......Page p0212.djvu
7.2. Poincare Spinors......Page p0214.djvu
7.3. Stokes Parameters......Page p0215.djvu
7.4. Polarizers and Phase Shifters......Page p0218.djvu
7.5. Coherent and Incoherent Superpositions......Page p0219.djvu
7.6. Problems......Page p0220.djvu
8.1. Maxwell's Macroscopic Equations......Page p0222.djvu
8.2. Linear, Isotropic Media......Page p0224.djvu
8.4. Directed Plane Waves......Page p0226.djvu
8.5. Waves in Conducting Media......Page p0229.djvu
8.6. Problems......Page p0235.djvu
9.1. Nonconducting Boundaries......Page p0237.djvu
9.2. Normal Incidence......Page p0244.djvu
9.3. Fresnel Equations......Page p0245.djvu
9.4. Conducting Surfaces......Page p0248.djvu
9.5. Wave Guides......Page p0255.djvu
9.6. TE and TM Modes......Page p0257.djvu
9.7. Problems......Page p0262.djvu
10. The Field of a Moving Charge......Page p0265.djvu
10.1. Lienard-Wiechert Potentials......Page p0266.djvu
10.2. The Electromagnetic Field......Page p0268.djvu
10.3. Example: Uniformly Accelerated Charge......Page p0276.djvu
10.4. Radiated Power......Page p0279.djvu
10.5. Green Functions......Page p0285.djvu
10.6. Fields from Currents......Page p0292.djvu
10.7. Virtual-Photon Streams......Page p0293.djvu
10.8. Review Questions......Page p0297.djvu
10.9. Problems......Page p0298.djvu
11.1. Static Polarizability......Page p0303.djvu
11.2. Atoms in Anisotropic Media......Page p0304.djvu
11.3. Scattering of Radiation by Bound Charge......Page p0306.djvu
11.4. Blue Sky......Page p0308.djvu
11.5. Scattering in a Magnetic Field......Page p0310.djvu
11.6. Drude Model of Van der Waals Forces......Page p0312.djvu
11.7. Diffraction......Page p0314.djvu
11.8. Linear Antenna......Page p0316.djvu
11.9. Problems......Page p0318.djvu
12.1. Introduction......Page p0321.djvu
12.2. Self Interaction......Page p0322.djvu
12.3. The Lorentz-Dirac Equation......Page p0326.djvu
12.4. Pathological Features......Page p0327.djvu
12.5. Eigenspinor Form......Page p0334.djvu
12.6. Conclusions......Page p0336.djvu
12.7. Problems......Page p0337.djvu
13.1. Spherical Harmonics......Page p0339.djvu
13.2. Ladder Operators......Page p0341.djvu
13.3. Rotations and Matrix Representations......Page p0349.djvu
13.4. Infinitesimal Generators......Page p0357.djvu
13.5. Multipoles of Charge Distributions......Page p0359.djvu
13.6. Problems......Page p0363.djvu
14.1. Wave Equation......Page p0365.djvu
14.2. Vector Spherical Harmonics......Page p0366.djvu
14.3. Spherical Bessel Functions......Page p0369.djvu
14.4. Electromagnetic Multipoles......Page p0371.djvu
14.5. Problems......Page p0372.djvu
A.1. Coordinate Systems in Physical Space......Page p0374.djvu
A.2. Gradient Operator......Page p0377.djvu
A.3. Spherical Coordinates......Page p0378.djvu
A.5. Cylindrical Coordinates......Page p0381.djvu
B. Appendix: Maple Worksheet rad3.mws......Page p0382.djvu
Bibliography......Page p0384.djvu
Index......Page p0387.djvu