B.Thide - Electromagnetic Field Theory

Hamilton density equations, 80 Hamilton equations, 72, 188 Hamilton function, 188 Hamilton gauge, 42 Hamiltonian, 188

Heaviside potential, 138 Helmholtz' theorem, 40 help vector, 117

Hertz' method, 116 Hertz' vector, 117 Hodge star operator, 18

homogeneous wave equation, 26 Huygen's principle, 43

identity element, 57 in a medium, 156

incoherent radiation, 150 indefinite norm, 53 index contraction, 52 index lowering, 52 induction field, 100

inertial reference frame, 49 inertial system, 49

inhomogeneous Helmholtz equation, 43 inhomogeneous time-independent wave

equation, 43 inhomogeneous wave equation, 43 inner product, 178

instantaneous, 140

interaction Lagrange density, 81 intermediate field, 103 invariant, 171

invariant line element, 55 inverse element, 57 irrotational, 5, 185

Kelvin function, 151 kinetic energy, 77, 187 kinetic momentum, 76 Kronecker delta, 173

Lagrange density, 78

Lagrange equations, 187

Lagrange function, 77, 187

Lagrangian, 77, 187

Laplace operator, 185 Laplacian, 185

Larmor formula for radiated power, 140 law of inertia, 49

Legendre polynomial, 118 Legendre transformation, 188 Levi-Civita tensor, 173

Liénard-Wiechert potentials, 64, 127, 137

light cone, 55 light-like interval, 55 line element, 178 linear mass density, 78

linearly polarised wave, 32 longitudinal component, 30 Lorentz boost parameter, 59 Lorentz force, 15, 93, 138 Lorentz gauge, 42

Lorentz gauge condition, 40, 62 Lorentz inhomogeneous wave equations,

41

Lorentz potential equations, 41 Lorentz space, 53, 170

Lorentz transformation, 51, 137 lowering of index, 176

M1 radiation, 123 Mach cone, 158

macroscopic Maxwell equations, 153 magnetic charge density, 17 magnetic current density, 17 magnetic dipole moment, 90, 123 magnetic dipole radiation, 123 magnetic displacement current, 19 magnetic field, 7

magnetic field energy, 93 magnetic field intensity, 91 magnetic flux, 13 magnetic flux density, 8 magnetic induction, 8 magnetic monopoles, 17 magnetic permeability, 153 magnetic susceptibility, 91 magnetisation, 90 magnetisation currents, 90

magnetising field, 16, 91 magnetostatic vector potential, 38 magnetostatics, 6

massive photons, 85 mathematical group, 57 matrix form, 172 Maxwell stress tensor, 94

Maxwell's macroscopic equations, 16, 92

Maxwell's microscopic equations, 15 Maxwell-Lorentz equations, 15 mechanical Lagrange density, 81 metric, 170, 178

metric tensor, 52, 170, 176 Minkowski equation, 72 Minkowski space, 58 mixed four-tensor field, 176 mixing angle, 18

momentum theorem in Maxwell's theory, 95

monochromatic, 97

multipole expansion, 116, 119

near zone, 103 Newton's first law, 49

Newton-Lorentz force equation, 72 non-Euclidean space, 53 non-linear effects, 11

norm, 52, 180 null vector, 55

observation point, 4 Ohm's law, 11

one-dimensional wave equation, 31 outer product, 181

Parseval's identity, 107, 144, 152 phase velocity, 153

photon, 145

physical measurable, 34 plane polarised wave, 32 plasma, 155

plasma frequency, 155 Poisson equation, 137 Poisson's equation, 37

polar vector, 65, 182 polarisation charges, 89 polarisation currents, 90 polarisation potential, 117 polarisation vector, 117 positive definite, 58 positive definite norm, 53 potential energy, 77, 187 potential theory, 118 power flux, 93

Poynting vector, 93 Poynting's theorem, 93 Proca Lagrangian, 84 propagator, 44

proper time, 55 pseudo-Riemannian space, 58 pseudoscalar, 169 pseudoscalars, 182 pseudotensor, 169 pseudotensors, 182 pseudovector, 65, 169, 182

quadratic differential form, 54, 178 quantum mechanical nonlinearity, 4

radiation field, 100, 103, 131 radiation fields, 103 radiation gauge, 42 radiation resistance, 112 radius four-vector, 52

radius vector, 169 raising of index, 176 rank, 172

rapidity, 59 refractive index, 154

relative electric permittivity, 94 relative magnetic permeability, 94 relative permeability, 153 relative permittivity, 153 Relativity principle, 50 relaxation time, 27

rest mass density, 81 retarded Coulomb field, 103 retarded potentials, 46 retarded relative distance, 127

retarded time, 45 Riemannian metric, 54 Riemannian space, 52, 170 row vector, 169

scalar, 169, 184 scalar field, 56, 171 scalar product, 178 shock front, 158 signature, 53, 177

simultaneous coordinate, 135 skew-symmetric, 65

skin depth, 34 source point, 4

space components, 53 space-like interval, 55 space-time, 53

special theory of relativity, 49 spherical Bessel function of the first

kind, 118

spherical Hankel function of the first kind, 118

spherical waves, 106 standing wave, 110 super-potential, 117

synchrotron radiation, 147, 150 synchrotron radiation lobe width, 149

telegrapher's equation, 31, 153 temporal dispersive media, 12 temporal gauge, 42

tensor, 169

tensor contraction, 176 tensor field, 172 tensor notation, 173 tensor product, 181

three-dimensional functional derivative, 80

time component, 53 time-harmonic wave, 27

time-independent diffusion equation, 28 time-independent telegrapher's equation,

32

time-independent wave equation, 28 time-like interval, 55

total charge, 87 transverse components, 31 transverse gauge, 42

vacuum permeability, 6 vacuum permittivity, 3 vacuum polarisation effects, 4 vacuum wave number, 28

ˇ

Vavilov-Cerenkov radiation, 156, 158 vector, 169

vector product, 181 velocity field, 131

virtual simultaneous coordinate, 128, 131

wave equations, 25 wave vector, 31, 154 world line, 57

Young's modulus, 78

Yukawa meson field, 84