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Articles

Doppler Shift from a Composition of Boosts with Thomas Rotation: a Spacetime Algebra Approach

Pages 941-953 | Published online: 03 Apr 2012

References

  • Papas , C. H. 1988 . Theory of Electromagnetic Wave Propagation 226 Dover , New York
  • Jackson , J. D. 1999 . Classical Electrodynamics , 3rd ed. , 530 New York : Wiley .
  • Kong , J. A. 2005 . Electromagnetic Wave Theory , 899 Cambridge , Massachusetts : EMW Publishing .
  • Ellis , G. F. R. and Williams , R. M. 2000 . Flat and Curved Space-Times , 2nd ed. , 49 – 121 . Oxford : Oxford University Press .
  • Rindler , W. 1991 . Introduction to Special Relativity , 2nd ed. , 64 Oxford : Oxford University Press .
  • Woodhouse , N. M. J. 2003 . Special Relativity , 3rd ed. , 142 London : Springer .
  • Schwarz , P. M. and Schwarz , J. H. 2004 . Special Relativity:F rom Einstein to Strings , 125 – 126 . Cambridge : Cambridge University Press .
  • Chen , H. C. 1983 . Theory of Electromagnetic Waves:A Coordinate-Free Approach , 1 – 57 . New York : McGraw-Hill .
  • Lindell , I. V. 1992 . Methods for Electromagnetic Field Analysis , 17 – 52 . New York : IEEE Press .
  • Minkowski , H. 1952 . “ Space and time ” . In The Principle of Relativity Edited by: Lorentz , H. A. , Einstein , A. , Minkowski , H. and Weyl , H. 73 – 91 . Dover , New York
  • Lounesto , P. 2001 . Clifford Algebras and Spinors , 2nd ed. , 98 Cambridge : Cambridge University Press .
  • Hestenes , D. 2003 . Spacetime physics with geometric algebra . Am. J. Phys., Vol , 71 : 691 – 714 .
  • Hestenes , D. and Bobczyk , G. 1984 . Clifford Algebra to Geometric Calculus:A Unified Language for Mathematics and Physics , Dordrecht : Kluwer Academic Publishers .
  • Doran , C. and Lasenby , A. 2003 . Geometric Algebra for Physicists , 126 – 166 . Cambridge : Cambridge University Press .
  • Thomas , L. H. 1927 . The kinematics of an electron with an axis . Philos. Mag. , 3 : 1 – 23 .
  • Wigner , E. P. 1939 . On unitary representations of the inhomogeneous Lorentz group . Ann. Math. , 40 : 149 – 204 .
  • Ungar , A. A. 1997 . Thomas precession: its underlying gyrogroup axioms and their use in hyperbolic geometry and relativistic physics . Found. Phys. , 27 : 881 – 951 .
  • Costella , J. P. , McKellar , B. H. J. , Rawlinson , A. A. and Stephenson , G. J. Jr. 2001 . The Thomas rotation . Am. J. Phys. , 69 : 837 – 847 .
  • Kennedy , W. L. 2002 . Thomas rotation: a Lorentz matrix approach . Eur. J. Phys. , 23 : 235 – 247 .
  • Rhodes , J. A. and Semon , M. D. 2004 . Relativistic velocity space, Wigner rotation, and Thomas precession . Am. J. Phys. , 77 : 943 – 960 .
  • Paiva , C. R. and Ribeiro , M. A. “ Generalized relativistic velocity addition with spacetime algebra ” . at http://arxiv.org/ftp/physics/papers/0511/0511247.pdf.
  • Paiva , C. R. “ Passive Lorentz transformations with spacetime algebra ” . at http://arxiv.org/ftp/physics/papers/0508/ 0508225.pdf.
  • Lee , A. R. and Kalotas , T. M. 1975 . Lorentz transformations from the first postulate . Am. J. Phys. , 43 : 434 – 437 .
  • Lévy-Leblond , J-M. 1976 . One more derivation of the Lorentz transformation . Am. J. Phys. , 44 : 271 – 277 .
  • Mermin , N. D. 1984 . Relativity without light . Am. J. Phys. , 52 : 119 – 124 .
  • Jackson , J. D. 1999 . Classical Electrodynamics , 3rd ed. , 548 – 566 . New York : Wiley .
  • Baylis , W. E. 2004 . “ Applications of Clifford algebras in physics ” . In Lectures on Clifford (Geometric) Algebras and Applications , Edited by: Ablamowicz , R. and Bobczyk , G. 91 – 133 . Boston : Birkh¨auser .
  • Puska , P. 2001 . “ Covariant isotropic constitutive relations in Clifford’s geometric algebra ” . In PIER 32 — Geometric Methods in Computational Electromagnetics , Edited by: Teixeira , F. L. and Kong , J. A. 413 – 428 . Cambridge , MA : EMW Publishing . http://ceta.mit.edu/PIER/pier32/16.puska.pdf.
  • Warnick , K. F. , Selfridge , R. H. and Arnold , D. V. Teaching electromagnetic field theory using differential forms . IEEE Trans. Ed. , 40 53 – 68 .
  • Lindell , I. V. 2004 . Differential Forms in Electromagnetics , Piscataway , NJ : IEEE Press .
  • Morita , S. 2001 . Geometry of Differential Forms , Providence , Rhode Island : American Mathematical Society .

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