References - Springer978-3-642-28329-1/1.pdf · References 1. V.I. Arnold, Mathematical Methods of...
Transcript of References - Springer978-3-642-28329-1/1.pdf · References 1. V.I. Arnold, Mathematical Methods of...
References
1. V.I. Arnold, Mathematical Methods of Classical Mechanics (Springer, Berlin, 1980)2. A. Aspect, J. Dalibard, G. Roger, Experimental test of Bell’s in-equalities using time-varying
analyzers. Phys. Rev. Lett. 49, 1804–1807 (1982)3. J. Bailey et al., Il Nuovo Cimento 9A, 369 (1972)4. J.S. Bell, On the Einstein–Podolsky–Rosen paradox, Physics 1, 195–200 (1964), reprinted
in [5]5. J.S. Bell, Speakable and Unspeakable in Quantum Mechanics (Cambridge University Press,
Cambridge, 1987)6. M.V. Berry, Regular and irregular motion, in Topics in Nonlinear Dynamics. Amer. Inst.
Phys. Conf. Proceedings Nr, ed. by S. Jorna, vol. 46, (1978) p. 167. H. Bondi, Relativity and Common Sense (Heinemann, London, 1965)8. I. Ciufolini, J.A. Wheeler, Gravitation and Inertia, Princeton Series in Physics (Princeton
University Press, Princeton, 1995)9. J.F. Clausner, M.A. Horne, A. Shimony, R.A. Holt, Proposed experiment to test local hidden-
variable theories. Phys. Rev. Lett 23, 880–884 (1969)10. R. Courant, D. Hilbert, Methods of Mathematical Physics II (Wiley, Chichester, 1953)11. N. Dragon, BRST Cohomology, http://www.itp.uni-hannover.de/dragon12. N. Dragon, N. Mokros, Relativistic Flight through Stonehenge (1999), http://www.itp.uni-
hannover.de/dragon13. C.W.F. Everitt et al., Gravity probe B: final results of a space experiment to test general
relativity. Phys. Rev. Lett. 106, 221–101 (2011)14. J.C. Hafele, R.E. Keating, Around-the-world atomic clocks: predicted relativistic time gains.
Science 177, 166–167 (1972): Around-the-world atomic clocks: observed relativistic timevalues, Science 177, 168–170 (1972)
15. R.A. d’Inverno, Introducing Einstein’s Relativity (Oxford University Press, Oxford, 1992)16. J.D. Jackson, L.B. Okun, Historical roots of gauge invariance. Rev. Mod. Phys. 73, 663–680
(2001)17. R. Kippenhahn, Light from the Depths of Time (Springer, Berlin, 1987)18. A. Lampa, Wie erscheint nach der Relativitätstheorie ein bewegter Stab einem ruhenden
Beobachter? Zeitschrift for Physik 27, 138–148 (1924)19. D.-E. Liebscher, Einstein’s Relativity and the Geometries of the Plane (Wiley-VCH Verlag
GmbH, Germany, 1998)20. L.V. Lorenz, On the identity of the vibrations of light with electrical currents. Phil. Mag. Ser.
4(34), 287–301 (1867)
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
139
21. J. Moser, Stable and Random Motion in Dynamical Systems (Princeton University Press,Princeton, 1973)
22. T. Needham, Visual Complex Analysis (Clarendon Press, Oxford, 1997)23. P. Nemec, http://www.ohg-sb.de/lehrer/nemec/relativ.htmwww.ohg-sb.de/lehrer/nemec/
relativ.htm24. E. Noether, Invariante Variationsprobleme, Nachrichten von der Königlichen Gesellschaft
der Wissenschaften zu Göttingen, Mathematisch-physikalische Klasse, pp. 235 – 257 (1918)25. J. O’Connor, E. Robertson, The MacTutor History of Mathematics Archive, http://www-
groups.dcs.st-and.ac.uk/history/BiogIndex.html26. P.J. Olver, Applications of Lie Groups to Differential Equations (Springer, Berlin, 1986)27. B. Parkinson, J. Spilker (eds.), Global Positioning System: Theory and Applications, vol. I.
(American Institute of Aeronautics and Astronautics, Washington, 1996)28. Particle Data Group, K. Nakamura et al., J. Phys. G 37 075021 (2010), http://pdg.lbl.gov29. R. Penrose, The apparent shape of a relativistically moving sphere. Proc. Camb. Phil. Soc. 55,
137–139 (1959)30. G. Seeber, Satellite Geodesy: Foundations, Methods and Applications (de Gruyther, New
York, 1993)31. L. Stodolsky, The speed of light and the speed of neutrinos. Phys. Lett. B 201, 353 (1988)32. J.L. Synge, Relativity: The General Theory (North-Holland, Amsterdam, 1964) (The name
Synge is pronounced sing)33. J. Terrell, Invisibility of Lorentz Contraction. Phys. Rev. 116, 1041–1045 (1959)34. C.M. Will, Theory and Experiment in Gravitational Physics (Cambridge University Press,
Cambridge, 1993)35. C.M. Will, The Confrontation between General Relativity and Experiment, http://arxiv.org/
abs/gr-qc/010303636. http://mathworld.wolfram.com/Hyperboloid.html37. M.J.W. Nicholas, Special Relativity, Lecture Notes in Physics m6 (Springer, Berlin, 1992)
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