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140 References

Index

SymbolsBe,y, 100MR,y[/], 102h, 104dm

n, 86, 123oL

oxm, 75, 115

O(p,q), 126SL(2, C), 133–137SO(p,q), 127~dk, 106eijk, 89–90c, 9–10dt, 72, 114Rp,q, 126Z2, 132

AAberration, 54–59, 137Acceleration, 4, 7, 69, 121Action, 75, 115Active transformation, 50Angular momentum, 83Axial vector, 90

BBackground radiation, 2, 85Bell’s inequality, 15, 18Boost, 51, 136

CCanonically conjugate

momentum, 81

Charge conservation, 94Comoving, 10Compton scattering, 65–66Conformal, 57, 117Conserved quantity, 59–66, 77–86Continuity equation, 94Contragredient, 87Coulomb potential, 99Cyclic variable, 81

Dd’Alembert operator, 104Decay, 64Degrees of freedom, 71Domain of dependence, 97, 105Doppler effect, 22, 27, 35, 54–59

EElectron radius, 122E = mc2, 63Energy, 59–66, 82, 83, 94, 95, 117Energy-momentum

tensor, 95, 117, 119Equilocal, 12Equitemporal, 12Euler derivative, 75, 115Euler-Lagrange equation, 75, 115

FFour-momentum, 63Four-potential, 103Functional, 73, 115Functional derivative, 74, 75

N. Dragon, The Geometry of Special Relativity—a Concise Course,SpringerBriefs in Physics, DOI: 10.1007/978-3-642-28329-1,� The Author(s) 2012

141

GGauge transformation, 104, 118Group, 53, 77

HHuygen’s principle, 106Hyperbola, 43

IImage of a moving body, 54Improvement terms, 116Induced representation, 78Inertia, 64Infinitesimal transformations, 79, 116

JJet space, 71, 114

LLagrangian, 73, 82, 115Laplace equation, 100Length contraction, 33–35, 45, 46Length squared, 40–44, 67–69Liénard Wiechert potential, 119Lift, 71, 114Light angle, 12Light coordinates, 38Light cone, 2, 6–9, 97, 105Lightlike, 41, 63Limit velocity, 14Local functional, 73Lorentz condition, 104Lorentz force, 91, 96Lorentz transformation, 49–53, 137Luminosity, 59

MMass, 62–66Maximum–minimum-principle, 102Maxwell equations, 7, 91Measuring rod, 33, 35Meter, 9Michelson, 6, 9Minkowski space, 126Möbius transformation, 123, 136–137Momentum, 59–66, 81, 95, 117Muon, 69

NNeutrino, 7, 85Noether theorem, 77–80, 116–118Normal subgroup, 132

OOne-dimensional motion, 83Orthogonality relation, 88, 124

PPassive transformation, 50Pauli matrices, 131Permutation, 103Photon, 7, 15–19, 54, 63, 65Poincaré transformation, 53Poisson equation, 100Poynting vector, 96Pressure, 96

RRapidity, 28Realisation, 78Referee, 11, 22Representation, 60, 78, 87Rigid body, 9, 15Rømer, 6

SSecond, 9Simultaneous, 10–15, 43Spacelike, 42, 97Spacetime, 1Speed of light, 6, 9Stereographic projection, 57Subgroup, 77Summation convention, 72, 123Superluminal speed, 15, 37Symmetry, 77, 79

TTachyon, 15, 65Teleportation, 15Tensor, 87Tensor product, 87Time dilation, 28, 35Timelike, 42Trace, 134

142 Index

Transformation, 77Twin paradox, 30–47

UUnimodular, 77Unitary transformation, 131, 133

VVelocity, 7, 9, 28, 53–54

WWave packet, 106Worldline, 7

Index 143